Subjects -> MATHEMATICS (Total: 1082 journals)
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MATHEMATICS (800 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 11)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 8)
Advances in Mathematics     Full-text available via subscription   (Followers: 17)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in Numerical Analysis     Open Access   (Followers: 9)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal   (Followers: 2)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 10)
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 9)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 3)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 12)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 5)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 1)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
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: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 1)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 22)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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  
Ciencia     Open Access   (Followers: 1)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
CODEE Journal     Open Access   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
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: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Desimal : Jurnal Matematika     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Computational Optimization and Applications
Journal Prestige (SJR): 1.127
Citation Impact (citeScore): 2
Number of Followers: 9  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003
Published by Springer-Verlag Homepage  [2624 journals]
  • Saddle points of rational functions
    • Abstract: This paper concerns saddle points of rational functions, under general constraints. Based on optimality conditions, we propose an algorithm for computing saddle points. It uses Lasserre’s hierarchy of semidefinite relaxation. The algorithm can get a saddle point if it exists, or it can detect its nonexistence if it does not. Numerical experiments show that the algorithm is efficient for computing saddle points of rational functions.
      PubDate: 2020-04-01
       
  • Stochastic structured tensors to stochastic complementarity problems
    • Abstract: This paper is concerned with the stochastic structured tensors to stochastic complementarity problems. The definitions and properties of stochastic structured tensors, such as the stochastic strong P-tensors, stochastic P-tensors, stochastic \(P_{0}\)-tensors, stochastic strictly semi-positive tensors and stochastic S-tensors are given. It is shown that the expected residual minimization formulation (ERM) of the stochastic structured tensor complementarity problem has a nonempty and bounded solution set. Interestingly, we partially answer the open questions proposed by Che et al. (Optim Lett 13:261–279, 2019). We also consider the expected value method of stochastic structured tensor complementarity problem with finitely many elements probability space. Finally, based on the expected residual minimization formulation (ERM) of the stochastic structured tensor complementarity problem, a projected gradient method is proposed for solving the stochastic structured tensor complementarity problem and the related numerical results are also given to show the efficiency of the proposed method.
      PubDate: 2020-04-01
       
  • Higher-degree tensor eigenvalue complementarity problems
    • Abstract: In this paper, we study the higher-degree tensor eigenvalue complementarity problem (HDTEiCP). We give an upper bound for the number of the higher-degree complementarity eigenvalues for the generic HDTEiCP. A semidefinite relaxation algorithm is proposed for computing all the higher-degree complementarity eigenvalues sequentially, as well as the corresponding eigenvectors, and the convergence of the algorithm is discussed. Some numerical results are also given.
      PubDate: 2020-04-01
       
  • Iterative methods for computing U-eigenvalues of non-symmetric complex
           tensors with application in quantum entanglement
    • Abstract: The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a non-symmetric complex tensor and unitary symmetric eigenpairs (US-eigenpairs) of its symmetric embedding tensor is established. An Algorithm 3.1 is given to compute the U-eigenvalues of non-symmetric complex tensors by means of symmetric embedding. Another Algorithm 3.2, is proposed to directly compute the U-eigenvalues of non-symmetric complex tensors, without the aid of symmetric embedding. Finally, a tensor version of the well-known Gauss–Seidel method is developed. Efficiency of these three algorithms are compared by means of various numerical examples. These algorithms are applied to compute the geometric measure of entanglement of quantum multipartite non-symmetric pure states.
      PubDate: 2020-04-01
       
  • SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0) -tensor
           detection
    • Abstract: \(\mathbf {P}\)-tensor and \(\mathbf {P}_0\)-tensor are introduced in tensor complementarity problem, which have wide applications in game theory. In this paper, we establish SDP relaxation algorithms for detecting \(\mathbf {P}(\mathbf {P}_0)\)-tensor. We first reformulate \(\mathbf {P}(\mathbf {P}_0)\)-tensor detection problem as polynomial optimization problems. Then we propose the SDP relaxation algorithms for solving the reformulated polynomial optimization problems. Numerical examples are reported to show the efficiency of the proposed algorithms.
      PubDate: 2020-04-01
       
  • Tensor neural network models for tensor singular value decompositions
    • Abstract: Tensor decompositions have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-one outer products using either the CANDECOMP/PARAFAC, the Tucker model, or some variations thereof. The motivation of these decompositions is to find an approximate representation for a given tensor. The main propose of this paper is to develop two neural network models for finding an approximation based on t-product for a given third-order tensor. Theoretical analysis shows that each of the neural network models ensures the convergence performance. The computer simulation results further substantiate that the models can find effectively the left and right singular tensor subspace.
      PubDate: 2020-04-01
       
  • A semidefinite relaxation method for second-order cone polynomial
           complementarity problems
    • Abstract: This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation, a semidefinite relaxation method is proposed by solving a finite number of semidefinite relaxations with some assumptions. Numerical experiments are given to show the efficiency of the method.
      PubDate: 2020-04-01
       
  • An inexact augmented Lagrangian method for computing strongly orthogonal
           decompositions of tensors
    • Abstract: A strongly orthogonal decomposition of a tensor is a rank one tensor decomposition with the two component vectors in each mode of any two rank one tensors are either colinear or orthogonal. A strongly orthogonal decomposition with few number of rank one tensors is favorable in applications, which can be represented by a matrix-tensor multiplication with orthogonal factor matrices and a sparse tensor; and such a decomposition with the minimum number of rank one tensors is a strongly orthogonal rank decomposition. Any tensor has a strongly orthogonal rank decomposition. In this article, computing a strongly orthogonal rank decomposition is equivalently reformulated as solving an optimization problem. Different from the ill-posedness of the usual optimization reformulation for the tensor rank decomposition problem, the optimization reformulation of the strongly orthogonal rank decomposition of a tensor is well-posed. Each feasible solution of the optimization problem gives a strongly orthogonal decomposition of the tensor; and a global optimizer gives a strongly orthogonal rank decomposition, which is however difficult to compute. An inexact augmented Lagrangian method is proposed to solve the optimization problem. The augmented Lagrangian subproblem is solved by a proximal alternating minimization method, with the advantage that each subproblem has a closed formula solution and the factor matrices are kept orthogonal during the iteration. Thus, the algorithm always can return a feasible solution and thus a strongly orthogonal decomposition for any given tensor. Global convergence of this algorithm to a critical point is established without any further assumption. Extensive numerical experiments are conducted, and show that the proposed algorithm is quite promising in both efficiency and accuracy.
      PubDate: 2020-04-01
       
  • On semi-infinite systems of convex polynomial inequalities and polynomial
           optimization problems
    • Abstract: We consider the semi-infinite system of polynomial inequalities of the form $$\begin{aligned} {{\mathbf {K}}}:=\{x\in {{\mathbb {R}}}^m\mid p(x,y)\ge 0,\quad \forall y\in S\subseteq {{\mathbb {R}}}^n\}, \end{aligned}$$where p(x, y) is a real polynomial in the variables x and the parameters y, the index set S is a basic semialgebraic set in \({{\mathbb {R}}}^n\), \(-p(x,y)\) is convex in x for every \(y\in S\). We propose a procedure to construct approximate semidefinite representations of \({{\mathbf {K}}}\). There are two indices to index these approximate semidefinite representations. As two indices increase, these semidefinite representation sets expand and contract, respectively, and can approximate \({{\mathbf {K}}}\) as closely as possible under some assumptions. In some special cases, we can fix one of the two indices or both. Then, we consider the optimization problem of minimizing a convex polynomial over \({{\mathbf {K}}}\). We present an SDP relaxation method for this optimization problem by similar strategies used in constructing approximate semidefinite representations of \({{\mathbf {K}}}\). Under certain assumptions, some approximate minimizers of the optimization problem can also be obtained from the SDP relaxations. In some special cases, we show that the SDP relaxation for the optimization problem is exact and all minimizers can be extracted.
      PubDate: 2020-04-01
       
  • Quantitative analysis for a class of two-stage stochastic linear
           variational inequality problems
    • Abstract: This paper considers a class of two-stage stochastic linear variational inequality problems whose first stage problems are stochastic linear box-constrained variational inequality problems and second stage problems are stochastic linear complementary problems having a unique solution. We first give conditions for the existence of solutions to both the original problem and its perturbed problems. Next we derive quantitative stability assertions of this two-stage stochastic problem under total variation metrics via the corresponding residual function. Moreover, we study the discrete approximation problem. The convergence and the exponential rate of convergence of optimal solution sets are obtained under moderate assumptions respectively. Finally, through solving a non-cooperative game in which each player’s problem is a parameterized two-stage stochastic program, we numerically illustrate our theoretical results.
      PubDate: 2020-03-21
       
  • Preface to the special issue on optimization with polynomials and tensors
    • PubDate: 2020-03-12
       
  • A computationally useful algebraic representation of nonlinear disjunctive
           convex sets using the perspective function
    • Abstract: Nonlinear disjunctive convex sets arise naturally in the formulation or solution methods of many discrete–continuous optimization problems. Often, a tight algebraic representation of the disjunctive convex set is sought, with the tightest such representation involving the characterization of the convex hull of the disjunctive convex set. In the most general case, this can be explicitly expressed through the use of the perspective function in higher dimensional space—the so-called extended formulation of the convex hull of a disjunctive convex set. However, there are a number of challenges in using this characterization in computation which prevents its wide-spread use, including issues that arise because of the functional form of the perspective function. In this paper, we propose an explicit algebraic representation of a fairly large class of nonlinear disjunctive convex sets using the perspective function that addresses this latter computational challenge. This explicit representation can be used to generate (tighter) algebraic reformulations for a variety of different problems containing disjunctive convex sets, and we report illustrative computational results using this representation for several nonlinear disjunctive problems.
      PubDate: 2020-03-12
       
  • Accelerating incremental gradient optimization with curvature information
    • Abstract: This paper studies an acceleration technique for incremental aggregated gradient (IAG) method through the use of curvature information for solving strongly convex finite sum optimization problems. These optimization problems of interest arise in large-scale learning applications. Our technique utilizes a curvature-aided gradient tracking step to produce accurate gradient estimates incrementally using Hessian information. We propose and analyze two methods utilizing the new technique, the curvature-aided IAG (CIAG) method and the accelerated CIAG (A-CIAG) method, which are analogous to gradient method and Nesterov’s accelerated gradient method, respectively. Setting \(\kappa\) to be the condition number of the objective function, we prove the R linear convergence rates of \(1 - \frac{4c_0 \kappa }{(\kappa +1)^2}\) for the CIAG method, and \(1 - \sqrt{\frac{c_1}{2\kappa }}\) for the A-CIAG method, where \(c_0,c_1 \le 1\) are constants inversely proportional to the distance between the initial point and the optimal solution. When the initial iterate is close to the optimal solution, the R linear convergence rates match with the gradient and accelerated gradient method, albeit CIAG and A-CIAG operate in an incremental setting with strictly lower computation complexity. Numerical experiments confirm our findings. The source codes used for this paper can be found on http://github.com/hoitowai/ciag/.
      PubDate: 2020-03-07
       
  • Empirical study of exact algorithms for the multi-objective spanning tree
    • Abstract: The multi-objective spanning tree (MoST) is an extension of the minimum spanning tree problem (MST) that, as well as its single-objective counterpart, arises in several practical applications. However, unlike the MST, for which there are polynomial-time algorithms that solve it, the MoST is NP-hard. Several researchers proposed techniques to solve the MoST, each of those methods with specific potentialities and limitations. In this study, we examine those methods and divide them into two categories regarding their outcomes: Pareto optimal sets and Pareto optimal fronts. To compare the techniques from the two groups, we investigated their behavior on 2, 3 and 4-objective instances from different classes. We report the results of a computational experiment on 8100 complete and grid graphs in which we analyze specific features of each algorithm as well as the computational effort required to solve the instances.
      PubDate: 2020-03-01
       
  • A conjugate direction based simplicial decomposition framework for solving
           a specific class of dense convex quadratic programs
    • Abstract: Many real-world applications can usually be modeled as convex quadratic problems. In the present paper, we want to tackle a specific class of quadratic programs having a dense Hessian matrix and a structured feasible set. We hence carefully analyze a simplicial decomposition like algorithmic framework that handles those problems in an effective way. We introduce a new master solver, called Adaptive Conjugate Direction Method, and embed it in our framework. We also analyze the interaction of some techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments based on a benchmark of almost 1400 instances from specific and generic quadratic problems. We show the efficiency and robustness of the method when compared to a commercial solver (Cplex).
      PubDate: 2020-03-01
       
  • A self-adaptive method for pseudomonotone equilibrium problems and
           variational inequalities
    • Abstract: In this paper, we introduce and analyze a new algorithm for solving equilibrium problem involving pseudomonotone and Lipschitz-type bifunction in real Hilbert space. The algorithm requires only a strongly convex programming problem per iteration. A weak and a strong convergence theorem are established without the knowledge of the Lipschitz-type constants of the bifunction. As a special case of equilibrium problem, the variational inequality is also considered. Finally, numerical experiments are performed to illustrate the advantage of the proposed algorithm.
      PubDate: 2020-03-01
       
  • Optimally linearizing the alternating direction method of multipliers for
           convex programming
    • Abstract: The alternating direction method of multipliers (ADMM) is being widely used in a variety of areas; its different variants tailored for different application scenarios have also been deeply researched in the literature. Among them, the linearized ADMM has received particularly wide attention in many areas because of its efficiency and easy implementation. To theoretically guarantee convergence of the linearized ADMM, the step size for the linearized subproblems, or the reciprocal of the linearization parameter, should be sufficiently small. On the other hand, small step sizes decelerate the convergence numerically. Hence, it is interesting to probe the optimal (largest) value of the step size that guarantees convergence of the linearized ADMM. This analysis is lacked in the literature. In this paper, we provide a rigorous mathematical analysis for finding this optimal step size of the linearized ADMM and accordingly set up the optimal version of the linearized ADMM in the convex programming context. The global convergence and worst-case convergence rate measured by the iteration complexity of the optimal version of linearized ADMM are proved as well.
      PubDate: 2020-03-01
       
  • On the tensor spectral p -norm and its dual norm via partitions
    • Abstract: This paper presents a generalization of the spectral norm and the nuclear norm of a tensor via arbitrary tensor partitions, a much richer concept than block tensors. We show that the spectral p-norm and the nuclear p-norm of a tensor can be lower and upper bounded by manipulating the spectral p-norms and the nuclear p-norms of subtensors in an arbitrary partition of the tensor for \(1\le p\le \infty\). Hence, it generalizes and answers affirmatively the conjecture proposed by Li (SIAM J Matrix Anal Appl 37:1440–1452, 2016) for a tensor partition and \(p=2\). We study the relations of the norms of a tensor, the norms of matrix unfoldings of the tensor, and the bounds via the norms of matrix slices of the tensor. Various bounds of the tensor spectral and nuclear norms in the literature are implied by our results.
      PubDate: 2020-02-20
       
  • Solution methods for a min–max facility location problem with regional
           customers considering closest Euclidean distances
    • Abstract: We study a facility location problem where a single facility serves multiple customers each represented by a (possibly non-convex) region in the plane. The aim of the problem is to locate a single facility in the plane so that the maximum of the closest Euclidean distances between the facility and the customer regions is minimized. Assuming that each customer region is mixed-integer second order cone representable, we firstly give a mixed-integer second order cone programming formulation of the problem. Secondly, we consider a solution method based on the Minkowski sums of sets. Both of these solution methods are extended to the constrained case in which the facility is to be located on a (possibly non-convex) subset of the plane. Finally, these two methods are compared in terms of solution quality and time with extensive computational experiments.
      PubDate: 2020-01-04
       
  • Secant update version of quasi-Newton PSB with weighted multisecant
           equations
    • Abstract: Quasi-Newton methods are often used in the frame of non-linear optimization. In those methods, the quality and cost of the estimate of the Hessian matrix has a major influence on the efficiency of the optimization algorithm, which has a huge impact for computationally costly problems. One strategy to create a more accurate estimate of the Hessian consists in maximizing the use of available information during this computation. This is done by combining different characteristics. The Powell-Symmetric-Broyden method (PSB) imposes, for example, the satisfaction of the last secant equation, which is called secant update property, and the symmetry of the Hessian (Powell in Nonlinear Programming 31–65, 1970). Imposing the satisfaction of more secant equations should be the next step to include more information into the Hessian. However, Schnabel proved that this is impossible (Schnabel in quasi-Newton methods using multiple secant equations, 1983). Penalized PSB (pPSB), works around the impossibility by giving a symmetric Hessian and penalizing the non-satisfaction of the multiple secant equations by using weight factors (Gratton et al. in Optim Methods Softw 30(4):748–755, 2015). Doing so, he loses the secant update property. In this paper, we combine the properties of PSB and pPSB by adding to pPSB the secant update property. This gives us the secant update penalized PSB (SUpPSB). This new formula that we propose also avoids matrix inversions, which makes it easier to compute. Next to that, SUpPSB also performs globally better compared to pPSB.
      PubDate: 2020-01-02
       
 
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