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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (651 journals)
    - MATHEMATICS (GENERAL) (42 journals)
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MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Computational Optimization and Applications
  [SJR: 1.481]   [H-I: 54]   [7 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003
   Published by Springer-Verlag Homepage  [2353 journals]
  • Forward–backward quasi-Newton methods for nonsmooth optimization
           problems
    • Authors: Lorenzo Stella; Andreas Themelis; Panagiotis Patrinos
      Pages: 443 - 487
      Abstract: Abstract The forward–backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward–backward envelope (FBE). This allows to extend algorithms for smooth unconstrained optimization and apply them to nonsmooth (possibly constrained) problems. Since the FBE can be computed by simply evaluating forward–backward steps, the resulting methods rely on a similar black-box oracle as FBS. We propose an algorithmic scheme that enjoys the same global convergence properties of FBS when the problem is convex, or when the objective function possesses the Kurdyka–Łojasiewicz property at its critical points. Moreover, when using quasi-Newton directions the proposed method achieves superlinear convergence provided that usual second-order sufficiency conditions on the FBE hold at the limit point of the generated sequence. Such conditions translate into milder requirements on the original function involving generalized second-order differentiability. We show that BFGS fits our framework and that the limited-memory variant L-BFGS is well suited for large-scale problems, greatly outperforming FBS or its accelerated version in practice, as well as ADMM and other problem-specific solvers. The analysis of superlinear convergence is based on an extension of the Dennis and Moré theorem for the proposed algorithmic scheme.
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9912-y
      Issue No: Vol. 67, No. 3 (2017)
       
  • Further properties of the forward–backward envelope with applications to
           difference-of-convex programming
    • Authors: Tianxiang Liu; Ting Kei Pong
      Pages: 489 - 520
      Abstract: Abstract In this paper, we further study the forward–backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358–2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward–backward envelope to be a level-bounded and Kurdyka–Łojasiewicz function with an exponent of \(\frac{1}{2}\) ; these results are important for the efficient minimization of the forward–backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward–backward envelope. Our preliminary numerical results on randomly generated instances of large-scale \(\ell _{1-2}\) regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536–A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479–2493, 2009).
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9900-2
      Issue No: Vol. 67, No. 3 (2017)
       
  • Total variation image deblurring with space-varying kernel
    • Authors: Daniel O’Connor; Lieven Vandenberghe
      Pages: 521 - 541
      Abstract: Abstract Image deblurring techniques based on convex optimization formulations, such as total-variation deblurring, often use specialized first-order methods for large-scale nondifferentiable optimization. A key property exploited in these methods is spatial invariance of the blurring operator, which makes it possible to use the fast Fourier transform (FFT) when solving linear equations involving the operator. In this paper we extend this approach to two popular models for space-varying blurring operators, the Nagy–O’Leary model and the efficient filter flow model. We show how splitting methods derived from the Douglas–Rachford algorithm can be implemented with a low complexity per iteration, dominated by a small number of FFTs.
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9901-1
      Issue No: Vol. 67, No. 3 (2017)
       
  • $$S_{1/2}$$ S 1 / 2 regularization methods and fixed point algorithms for
           affine rank minimization problems
    • Authors: Dingtao Peng; Naihua Xiu; Jian Yu
      Pages: 543 - 569
      Abstract: Abstract The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten \(q~ (0<q<1)\) quasi-norm to approximate the rank of a matrix, in this paper we use the Schatten 1 / 2 quasi-norm approximation which is a better approximation than the nuclear norm but leads to a nonconvex, nonsmooth and non-Lipschitz optimization problem. It is important that we give a global necessary optimality condition for the \(S_{1/2}\) regularization problem by virtue of the special objective function. This is very different from the local optimality conditions usually used for the general \(S_q\) regularization problems. Explicitly, the global necessary optimality condition for the \(S_{1/2}\) regularization problem is a fixed point inclusion associated with the singular value half thresholding operator. Naturally, we propose a fixed point iterative scheme for the problem. We also provide the convergence analysis of this iteration. By discussing the location and setting of the optimal regularization parameter as well as using an approximate singular value decomposition procedure, we get a very efficient algorithm, half norm fixed point algorithm with an approximate SVD (HFPA algorithm), for the \(S_{1/2}\) regularization problem. Numerical experiments on randomly generated and real matrix completion problems are presented to demonstrate the effectiveness of the proposed algorithm.
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9898-5
      Issue No: Vol. 67, No. 3 (2017)
       
  • New subgradient extragradient methods for common solutions to equilibrium
           problems
    • Authors: Dang Van Hieu
      Pages: 571 - 594
      Abstract: Abstract In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems in Hilbert spaces. The proposed algorithms originate from previously known results for variational inequalities and can be considered as modifications of extragradient methods for equilibrium problems. Theorems of strong convergence are established under the standard assumptions imposed on bifunctions. Some numerical experiments are given to illustrate the convergence of the new algorithms and to compare their behavior with other algorithms.
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9899-4
      Issue No: Vol. 67, No. 3 (2017)
       
  • Generalized Krasnoselskii–Mann-type iterations for nonexpansive
           mappings in Hilbert spaces
    • Authors: Christian Kanzow; Yekini Shehu
      Pages: 595 - 620
      Abstract: Abstract The Krasnoselskii–Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a new inexact Krasnoselskii–Mann iteration and prove weak convergence under certain accuracy criteria on the error resulting from the inexactness. We also show strong convergence for a modified inexact Krasnoselskii–Mann iteration under suitable assumptions. The convergence results generalize existing ones from the literature. Applications are given to the Douglas–Rachford splitting method, the Fermat–Weber location problem as well as the alternating projection method by John von Neumann.
      PubDate: 2017-07-01
      DOI: 10.1007/s10589-017-9902-0
      Issue No: Vol. 67, No. 3 (2017)
       
  • A primal majorized semismooth Newton-CG augmented Lagrangian method for
           large-scale linearly constrained convex programming
    • Authors: Chengjing Wang; Peipei Tang
      Abstract: Abstract In this paper, we propose a primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming problems, especially for some difficult problems. The basic idea of this method is to apply the majorized semismooth Newton-CG augmented Lagrangian method to the primal convex problem. And we take two special nonlinear semidefinite programming problems as examples to illustrate the algorithm. Furthermore, we establish the global convergence and the iteration complexity of the algorithm. Numerical experiments demonstrate that our method works very well for the testing problems, especially for many ill-conditioned ones.
      PubDate: 2017-07-28
      DOI: 10.1007/s10589-017-9930-9
       
  • Shrinking gradient descent algorithms for total variation regularized
           image denoising
    • Authors: Mingqiang Li; Congying Han; Ruxin Wang; Tiande Guo
      Abstract: Abstract Total variation regularization introduced by Rudin, Osher, and Fatemi (ROF) is widely used in image denoising problems for its capability to preserve repetitive textures and details of images. Many efforts have been devoted to obtain efficient gradient descent schemes for dual minimization of ROF model, such as Chambolle’s algorithm or gradient projection (GP) algorithm. In this paper, we propose a general gradient descent algorithm with a shrinking factor. Both Chambolle’s and GP algorithm can be regarded as the special cases of the proposed methods with special parameters. Global convergence analysis of the new algorithms with various step lengths and shrinking factors are present. Numerical results demonstrate their competitiveness in computational efficiency and reconstruction quality with some existing classic algorithms on a set of gray scale images.
      PubDate: 2017-07-27
      DOI: 10.1007/s10589-017-9931-8
       
  • Variable neighborhood scatter search for the incremental graph drawing
           problem
    • Authors: Jesús Sánchez-Oro; Anna Martínez-Gavara; Manuel Laguna; Rafael Martí; Abraham Duarte
      Abstract: Abstract Automated graph-drawing systems utilize procedures to place vertices and arcs in order to produce graphs with desired properties. Incremental or dynamic procedures are those that preserve key characteristics when updating an existing drawing. These methods are particularly useful in areas such as planning and logistics, where updates are frequent. We propose a procedure based on the scatter search methodology that is adapted to the incremental drawing problem in hierarchical graphs. These drawings can be used to represent any acyclic graph. Comprehensive computational experiments are used to test the efficiency and effectiveness of the proposed procedure.
      PubDate: 2017-07-27
      DOI: 10.1007/s10589-017-9926-5
       
  • On the worst-case evaluation complexity of non-monotone line search
           algorithms
    • Authors: Geovani N. Grapiglia; Ekkehard W. Sachs
      Abstract: Abstract A general class of non-monotone line search algorithms has been proposed by Sachs and Sachs (Control Cybern 40:1059–1075, 2011) for smooth unconstrained optimization, generalizing various non-monotone step size rules such as the modified Armijo rule of Zhang and Hager (SIAM J Optim 14:1043–1056, 2004). In this paper, the worst-case complexity of this class of non-monotone algorithms is studied. The analysis is carried out in the context of non-convex, convex and strongly convex objectives with Lipschitz continuous gradients. Despite de nonmonotonicity in the decrease of function values, the complexity bounds obtained agree in order with the bounds already established for monotone algorithms.
      PubDate: 2017-07-26
      DOI: 10.1007/s10589-017-9928-3
       
  • MDTri: robust and efficient global mixed integer search of spaces of
           multiple ternary alloys
    • Authors: Peter A. Graf; Stephen Billups
      Abstract: Abstract Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles instead of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Finally, we offer an explanation of the efficacy of DIRECT—specifically, its balance of global and local search—by showing that “potentially optimal rectangles” of the original algorithm are akin to the Pareto front of the “multi-component optimization” of global and local search.
      PubDate: 2017-07-24
      DOI: 10.1007/s10589-017-9922-9
       
  • Using negative curvature in solving nonlinear programs
    • Authors: Donald Goldfarb; Cun Mu; John Wright; Chaoxu Zhou
      Abstract: Abstract Minimization methods that search along a curvilinear path composed of a non-ascent negative curvature direction in addition to the direction of steepest descent, dating back to the late 1970s, have been an effective approach to finding a stationary point of a function at which its Hessian is positive semidefinite. For constrained nonlinear programs arising from recent applications, the primary goal is to find a stationary point that satisfies the second-order necessary optimality conditions. Motivated by this, we generalize the approach of using negative curvature directions from unconstrained optimization to equality constrained problems and prove that our proposed negative curvature method is guaranteed to converge to a stationary point satisfying second-order necessary conditions.
      PubDate: 2017-07-22
      DOI: 10.1007/s10589-017-9925-6
       
  • On the use of the energy norm in trust-region and adaptive cubic
           regularization subproblems
    • Authors: E. Bergou; Y. Diouane; S. Gratton
      Abstract: Abstract We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called “subproblem” in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called “the model”. The latter is supposed to be adequate in a neighborhood of the current iterate. In this paper, we address an important practical question related with the choice of the norm for defining the neighborhood. More precisely, assuming here that the Hessian B of the model is symmetric positive definite, we propose the use of the so-called “energy norm”—defined by \(\Vert x\Vert _B= \sqrt{x^TBx}\) for all \(x \in \mathbb {R}^n\) —in both TR and ARC techniques. We show that the use of this norm induces remarkable relations between the trial step of both methods that can be used to obtain efficient practical algorithms. We furthermore consider the use of truncated Krylov subspace methods to obtain an approximate trial step for large scale optimization. Within the energy norm, we obtain line search algorithms along the Newton direction, with a special backtracking strategy and an acceptability condition in the spirit of TR/ARC methods. The new line search algorithm, derived by ARC, enjoys a worst-case iteration complexity of \(\mathcal {O}(\epsilon ^{-3/2})\) . We show the good potential of the energy norm on a set of numerical experiments.
      PubDate: 2017-07-21
      DOI: 10.1007/s10589-017-9929-2
       
  • Algorithms for generalized potential games with mixed-integer variables
    • Authors: Simone Sagratella
      Abstract: Abstract We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixed-integer variables, i.e., games in which some variables are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss–Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches.
      PubDate: 2017-07-18
      DOI: 10.1007/s10589-017-9927-4
       
  • Decomposition methods based on articulation vertices for degree-dependent
           spanning tree problems
    • Authors: Mercedes Landete; Alfredo Marín; José Luis Sainz-Pardo
      Abstract: Abstract Decomposition methods for optimal spanning trees on graphs are explored in this work. The attention is focused on optimization problems where the objective function depends only on the degrees of the nodes of the tree. In particular, we deal with the Minimum Leaves problem, the Minimum Branch Vertices problem and the Minimum Degree Sum problem. The decomposition is carried out by identifying the articulation vertices of the graph and then its blocks, solving certain subproblems on the blocks and then bringing together the optimal sub-solutions following adequate procedures. Computational results obtained using similar Integer Programming formulations for both the original and the decomposed problems show the advantage of the proposed methods on decomposable graphs.
      PubDate: 2017-07-13
      DOI: 10.1007/s10589-017-9924-7
       
  • Markov–Dubins path via optimal control theory
    • Authors: C. Yalçın Kaya
      Abstract: Abstract Markov–Dubins path is the shortest planar curve joining two points with prescribed tangents, with a specified bound on its curvature. Its structure, as proved by Dubins in 1957, nearly 70 years after Markov posed the problem of finding it, is elegantly simple: a selection of at most three arcs are concatenated, each of which is either a circular arc of maximum (prescribed) curvature or a straight line. The Markov–Dubins problem and its variants have since been extensively studied in practical and theoretical settings. A reformulation of the Markov–Dubins problem as an optimal control problem was subsequently studied by various researchers using the Pontryagin maximum principle and additional techniques, to reproduce Dubins’ result. In the present paper, we study the same reformulation, and apply the maximum principle, with new insights, to derive Dubins’ result again. We prove that abnormal control solutions do exist. We characterize these solutions, which were not studied adequately in the literature previously, as a concatenation of at most two circular arcs and show that they are also solutions of the normal problem. Moreover, we prove that any feasible path of the types mentioned in Dubins’ result is a stationary solution, i.e., that it satisfies the Pontryagin maximum principle. We propose a numerical method for computing Markov–Dubins path. We illustrate the theory and the numerical approach by three qualitatively different examples.
      PubDate: 2017-07-12
      DOI: 10.1007/s10589-017-9923-8
       
  • On the control of time discretized dynamic contact problems
    • Authors: Georg Müller; Anton Schiela
      Abstract: Abstract We consider optimal control problems with distributed control that involve a time-stepping formulation of dynamic one body contact problems as constraints. We link the continuous and the time-stepping formulation by a nonconforming finite element discretization and derive existence of optimal solutions and strong stationarity conditions. We use this information for a steepest descent type optimization scheme based on the resulting adjoint scheme and implement its numerical application.
      PubDate: 2017-07-07
      DOI: 10.1007/s10589-017-9918-5
       
  • Descent algorithm for nonsmooth stochastic multiobjective optimization
    • Authors: Fabrice Poirion; Quentin Mercier; Jean-Antoine Désidéri
      Abstract: Abstract An algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multiobjective optimization using the properties of a common descent vector defined in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example.
      PubDate: 2017-06-28
      DOI: 10.1007/s10589-017-9921-x
       
  • An interior-point implementation developed and tuned for radiation therapy
           treatment planning
    • Authors: Sebastiaan Breedveld; Bas van den Berg; Ben Heijmen
      Abstract: Abstract While interior-point methods share the same fundamentals, the implementation determines the actual performance. In order to attain the highest efficiency, different applications may require differently tuned implementations. In this paper we describe an implementation specifically designed for optimisation in radiation therapy. These problems are large-scale nonlinear (and sometimes nonconvex) constrained optimisation problems, consisting of both sparse and dense data. Several application-specific properties are exploited to enhance efficiency. Permuting, tiling and mixed precision arithmetic allow the algorithm to optimally process the mixed dense and sparse data matrices (making this step 2.2 times faster, and overall runtime reduction of \(55\%\) ) and scalability (16 threads resulted in a speed-up factor of 9.8 compared to singlethreaded performance, against a speed-up factor of 7.7 for the less optimised implementation). Predefined cost-functions are hard-coded and the computationally expensive second derivatives are written in canonical form, and combined if multiple cost-functions are defined for the same clinical structure. The derivatives are then computed using a scaled matrix–matrix product. A cheap initialisation strategy based on the background knowledge reduces the number of iterations by \(11\%\) . We also propose a novel combined Mehrotra–Gondzio approach. The algorithm is extensively tested on a dataset consisting of 120 patients, distributed over 6 tumour sites/approaches. This test dataset is made publicly available.
      PubDate: 2017-06-28
      DOI: 10.1007/s10589-017-9919-4
       
  • On the convergence of alternating minimization methods in variational PGD
    • Authors: A. El Hamidi; H. Ossman; M. Jazar
      Abstract: Abstract The approximation of solutions to partial differential equations by tensorial separated representations is one of the most efficient numerical treatment of high dimensional problems. The key step of such methods is the computation of an optimal low-rank tensor to enrich the obtained iterative tensorial approximation. In variational problems, this step can be carried out by alternating minimization (AM) technics, but the convergence of such methods presents a real challenge. In the present work, the convergence of rank-one AM algorithms for a class of variational linear elliptic equations is studied. More precisely, we show that rank-one AM-sequences are in general bounded in the ambient Hilbert tensor space and are compact if a uniform non-orthogonality condition between iterates and the reaction term is fulfilled. In particular, if a rank-one AM-sequence is weakly convergent then it converges strongly and the common limit is a solution of the rank-one optimization problem.
      PubDate: 2017-06-27
      DOI: 10.1007/s10589-017-9920-y
       
 
 
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