Subjects -> MATHEMATICS (Total: 1118 journals)
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    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (819 journals)                  1 2 3 4 5 | 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: 3)
Accounting Perspectives     Full-text available via subscription   (Followers: 9)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 17)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 9)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 13)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 8)
Advances in Complex Systems     Hybrid Journal   (Followers: 12)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 5)
Advances in Fixed Point Theory     Open Access   (Followers: 9)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 22)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 22)
Advances in Mathematical Physics     Open Access   (Followers: 10)
Advances in Mathematics     Full-text available via subscription   (Followers: 22)
Advances in Numerical Analysis     Open Access   (Followers: 8)
Advances in Operations Research     Open Access   (Followers: 14)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Porous Media     Full-text available via subscription   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 12)
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: 4)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access   (Followers: 1)
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: 8)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 2)
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: 9)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 10)
Analysis Mathematica     Full-text available via subscription  
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access   (Followers: 8)
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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 17)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 4)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 6)
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   (Followers: 1)
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: 2)
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: 16)
Applied Mathematics     Open Access   (Followers: 10)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 13)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 2)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 2)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 6)
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: 4)
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: 24)
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  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 4)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 7)
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: 6)
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: 3)
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 15)
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: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
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: 2)
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: 23)
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: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 3)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (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: 17)
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: 5)
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: 11)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 3)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 10)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 11)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access   (Followers: 1)
Contributions to Discrete Mathematics     Open Access   (Followers: 1)
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 14)
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)
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access   (Followers: 1)
Demographic Research     Open Access   (Followers: 16)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access   (Followers: 3)
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: 4)

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Computational Optimization and Applications
Journal Prestige (SJR): 1.127
Citation Impact (citeScore): 2
Number of Followers: 11  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003
Published by Springer-Verlag Homepage  [2658 journals]
  • Correction to: Globalized inexact proximal Newton-type methods for
           nonconvex composite functions

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      PubDate: 2021-11-01
       
  • Forward-reflected-backward method with variance reduction

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      Abstract: We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O(1/k) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.
      PubDate: 2021-11-01
       
  • Strengthened splitting methods for computing resolvents

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      Abstract: In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the notion of the “strengthening” of a set-valued operator, which can be viewed as a type of regularisation that preserves computational tractability. After deriving a number of iterative schemes through this framework, we demonstrate their application to best approximation problems, image denoising and elliptic PDEs.
      PubDate: 2021-11-01
       
  • Two new bidirectional search algorithms

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      Abstract: This paper presents two new bidirectional heuristic search algorithms for solving the shortest path problem on graphs: consistent-heuristic bucket-based bidirectional search (CBBS) and front-to-front GPU bidirectional search (FFGBS). CBBS uses a consistent heuristic and groups nodes into buckets that organize nodes based on estimated path cost and known heuristic errors. FFGBS splits the work between the CPU and GPU, with the GPU solving a front-to-front heuristic and the CPU choosing nodes to expand. This paper also includes a new front-to-front version of the GAP heuristic for the pancake problem that is efficient to solve on a GPU. Computational experiments for CBBS are performed on the pancake problem. CBBS is faster and requires less node expansions with the GAP-1 heuristic, compared to bidirectional state of the algorithms like DIBBS and DVCBS. Computational experiments for FFGBS are performed on the pancake problem and DIMACS road network, showing that FFGBS is consistently the fastest algorithm on all but the smallest pancake stacks when using the GAP-2 heuristic and is also the fastest algorithm on the largest road networks.
      PubDate: 2021-11-01
       
  • Newton-type methods near critical solutions of piecewise smooth nonlinear
           equations

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      Abstract: It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to corresponding reformulations of nonlinear complementarity problems.
      PubDate: 2021-11-01
       
  • Exploiting term sparsity in noncommutative polynomial optimization

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      Abstract: We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy features the exploitation of term sparsity hidden in the input data for eigenvalue and trace optimization problems. NCTSSOS complements the recent work that exploits correlative sparsity for noncommutative optimization problems by Klep et al. (MP, 2021), and is the noncommutative analogue of the TSSOS framework by Wang et al. (SIAMJO 31: 114–141, 2021, SIAMJO 31: 30–58, 2021). We also propose an extension exploiting simultaneously correlative and term sparsity, as done previously in the commutative case (Wang in CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization, 2020). Under certain conditions, we prove that the optima of the NCTSSOS hierarchy converge to the optimum of the corresponding dense semidefinite programming relaxation. We illustrate the efficiency and scalability of NCTSSOS by solving eigenvalue/trace optimization problems from the literature as well as randomly generated examples involving up to several thousand variables.
      PubDate: 2021-11-01
       
  • An augmented subgradient method for minimizing nonsmooth DC functions

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      Abstract: A method, called an augmented subgradient method, is developed to solve unconstrained nonsmooth difference of convex (DC) optimization problems. At each iteration of this method search directions are found by using several subgradients of the first DC component and one subgradient of the second DC component of the objective function. The developed method applies an Armijo-type line search procedure to find the next iteration point. It is proved that the sequence of points generated by the method converges to a critical point of the unconstrained DC optimization problem. The performance of the method is demonstrated using academic test problems with nonsmooth DC objective functions and its performance is compared with that of two general nonsmooth optimization solvers and five solvers specifically designed for unconstrained DC optimization. Computational results show that the developed method is efficient and robust for solving nonsmooth DC optimization problems.
      PubDate: 2021-11-01
       
  • The selection of the optimal parameter in the modulus-based matrix
           splitting algorithm for linear complementarity problems

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      Abstract: The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer Linear Algebra Appl 17: 917–933, 2010). This algorithm is parameter dependent, and previous studies mainly focus on giving the convergence interval of the iteration parameter. Yet the specific selection approach of the optimal parameter has not been systematically studied due to the nonlinearity of the algorithm. In this work, we first propose a novel and simple strategy for obtaining the optimal parameter of the MMS algorithm by merely solving two quadratic equations in each iteration. Further, we figure out the interval of optimal parameter which is iteration independent and give a practical choice of optimal parameter to avoid iteration-based computations. Compared with the experimental optimal parameter, the numerical results from three problems, including the Signorini problem of the Laplacian, show the feasibility, effectiveness and efficiency of the proposed strategy.
      PubDate: 2021-11-01
       
  • Two methods for the maximization of homogeneous polynomials over the
           simplex

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      Abstract: The paper deals with the numerical solution of the problem P to maximize a homogeneous polynomial over the unit simplex. We discuss the convergence properties of the so-called replicator dynamics for solving P. We further examine an ascent method, which also makes use of the replicator transformation. Numerical experiments with polynomials of different degrees illustrate the theoretical convergence results.
      PubDate: 2021-11-01
       
  • A distributed algorithm for high-dimension convex quadratically
           constrained quadratic programs

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      Abstract: We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by interior-point algorithms, high-dimension problems pose significant challenges to traditional algorithms that are mainly designed to be implemented on a single computing unit. The exploding volume of data (and hence, the problem size), however, may overwhelm any such units. In this paper, we propose a distributed algorithm for general, non-separable, high-dimension convex QCQPs, using a novel idea of predictor–corrector primal–dual update with an adaptive step size. The algorithm enables distributed storage of data as well as parallel, distributed computing. We establish the conditions for the proposed algorithm to converge to a global optimum, and implement our algorithm on a computer cluster with multiple nodes using message passing interface. The numerical experiments are conducted on data sets of various scales from different applications, and the results show that our algorithm exhibits favorable scalability for solving high-dimension problems.
      PubDate: 2021-10-12
       
  • Nonsmooth exact penalization second-order methods for incompressible
           bi-viscous fluids

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      Abstract: We consider the exact penalization of the incompressibility condition \(\text {div}(\mathbf {u})=0\) for the velocity field of a bi-viscous fluid in terms of the \(L^1\) –norm. This penalization procedure results in a nonsmooth optimization problem for which we propose an algorithm using generalized second-order information. Our method solves the resulting nonsmooth problem by considering the steepest descent direction and extra generalized second-order information associated to the nonsmooth term. This method has the advantage that the divergence-free property is enforced by the descent direction proposed by the method without the need of build-in divergence-free approximation schemes. The inexact penalization approach, given by the \(L^2\) -norm, is also considered in our discussion and comparison.
      PubDate: 2021-10-05
       
  • A data-driven approach for a class of stochastic dynamic optimization
           problems

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      Abstract: Dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use statistical predictive methods to capture the structure of the underlying stochastic process without taking into consideration estimation errors and model misspecification. In this context, we propose a data-driven prescriptive analytics framework aiming to integrate the machine learning and dynamic optimization machinery in a consistent and efficient way to build a bridge from data to decisions. The proposed framework tackles a relevant class of dynamic decision problems comprising many important practical applications. The basic building blocks of our proposed framework are: (1) a Hidden Markov Model as a predictive (machine learning) method to represent uncertainty; and (2) a distributionally robust dynamic optimization model as a prescriptive method that takes into account estimation errors associated with the predictive model and allows for control of the risk associated with decisions. Moreover, we present an evaluation framework to assess out-of-sample performance in rolling horizon schemes. A complete case study on dynamic asset allocation illustrates the proposed framework showing superior out-of-sample performance against selected benchmarks. The numerical results show the practical importance and applicability of the proposed framework since it extracts valuable information from data to obtain robustified decisions with an empirical certificate of out-of-sample performance evaluation.
      PubDate: 2021-09-28
       
  • A parallel splitting ALM-based algorithm for separable convex programming

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      Abstract: The augmented Lagrangian method (ALM) provides a benchmark for solving the canonical convex optimization problem with linear constraints. The direct extension of ALM for solving the multiple-block separable convex minimization problem, however, is proved to be not necessarily convergent in the literature. It has thus inspired a number of ALM-variant algorithms with provable convergence. This paper presents a novel parallel splitting method for the multiple-block separable convex optimization problem with linear equality constraints, which enjoys a larger step size compared with the existing parallel splitting methods. We first show that a fully Jacobian decomposition of the regularized ALM can contribute a descent direction yielding the contraction of proximity to the solution set; then, the new iterate is generated via a simple correction step with an ignorable computational cost. We establish the convergence analysis for the proposed method, and then demonstrate its numerical efficiency by solving an application problem arising in statistical learning.
      PubDate: 2021-09-25
       
  • $${\text {B}}$$ B -subdifferentials of the projection onto the matrix
           simplex

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      Abstract: An important tool in matrix optimization problems is the strong semismoothness of the projection mapping onto the cone of real symmetric positive semidefinite matrices, and the explicit formula for its \({\text {B}}\) (ouligand)-subdifferentials. In this paper, we examine the corresponding results for the so-called matrix simplex, that is, the set of real symmetric positive semidefinite matrices whose traces are equal to one. This result complements the current literature and enlarges the toolbox of matrix spectral operators whose \({\text {B}}\) -subdifferentials are explicitly formulated. Since the matrix simplex frequently arises in subproblems for solving matrix optimization problems, the derived results can potentially serve as a useful tool for efficiently solving these problems. As an illustration, we present a numerical example to demonstrate that the proposed approach can outperform the existing approaches which used projection mapping onto positive semidefinite matrix cone directly.
      PubDate: 2021-09-20
      DOI: 10.1007/s10589-021-00316-0
       
  • Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm
           regularization

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      Abstract: There has been much research about regularizing optimal portfolio selections through \(\ell _1\) norm and/or \(\ell _2\) -norm squared. The common consensuses are (i) \(\ell _1\) leads to sparse portfolios and there exists a theoretical bound that limits extreme shorting of assets; (ii) \(\ell _2\) (norm-squared) stabilizes the computation by improving the condition number of the problem resulting in strong out-of-sample performance; and (iii) there exist efficient numerical algorithms for those regularized portfolios with closed-form solutions each step. When combined such as in the well-known elastic net regularization, theoretical bounds are difficult to derive so as to limit extreme shorting of assets. In this paper, we propose a minimum variance portfolio with the regularization of \(\ell _1\) and \(\ell _2\) norm combined (namely \(\ell _{1, 2}\) -norm). The new regularization enjoys the best of the two regularizations of \(\ell _1\) norm and \(\ell _2\) -norm squared. In particular, we derive a theoretical bound that limits short-sells and develop a closed-form formula for the proximal term of the \(\ell _{1,2}\) norm. A fast proximal augmented Lagrange method is applied to solve the \(\ell _{1,2}\) -norm regularized problem. Extensive numerical experiments confirm that the new model often results in high Sharpe ratio, low turnover and small amount of short sells when compared with several existing models on six datasets.
      PubDate: 2021-09-15
      DOI: 10.1007/s10589-021-00312-4
       
  • Accelerating convergence of a globalized sequential quadratic programming
           method to critical Lagrange multipliers

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      Abstract: This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is equipped with a standard Armijo linesearch procedure for a nonsmooth exact penalty function. The specificity of considerations here is that the standard assumptions for local superlinear convergence of the method may be violated. The analysis focuses on the case when there exist critical Lagrange multipliers, and does not require regularity assumptions on the constraints or satisfaction of second-order sufficient optimality conditions. The results provide a basis for application of known acceleration techniques, such as extrapolation, and allow the formulation of algorithms that can outperform the standard SQP with BFGS approximations of the Hessian on problems with degenerate constraints. This claim is confirmed by some numerical experiments.
      PubDate: 2021-09-13
      DOI: 10.1007/s10589-021-00317-z
       
  • Two limited-memory optimization methods with minimum violation of the
           previous secant conditions

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      Abstract: Limited-memory variable metric methods based on the well-known Broyden-Fletcher-Goldfarb-Shanno (BFGS) update are widely used for large scale optimization. The block version of this update, derived for general objective functions in Vlček and Lukšan (Numerical Algorithms 2019), satisfies the secant conditions with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the secant conditions as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously used together with methods based on vector corrections for conjugacy. Here we combine two types of these corrections to satisfy the secant conditions with both the corrected and uncorrected (original) latest difference vectors. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
      PubDate: 2021-09-12
      DOI: 10.1007/s10589-021-00318-y
       
  • A proximal gradient method for control problems with non-smooth and
           non-convex control cost

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      Abstract: We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of \(L^p\) -type for \(p\in [0,1)\) . We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin’s maximum principle and weaker than L-stationarity.
      PubDate: 2021-09-03
      DOI: 10.1007/s10589-021-00308-0
       
  • On solving a class of fractional semi-infinite polynomial programming
           problems

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      Abstract: In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex polynomial inequalities. To solve such a problem, we first reformulate it to a pair of primal and dual conic optimization problems, which reduce to semidefinite programming (SDP) problems if we can bring sum-of-squares structures into the conic constraints. To this end, we provide a characteristic cone constraint qualification for convex semi-infinite programming problems to guarantee strong duality and also the attainment of the solution in the dual problem, which is of its own interest. In this framework, we first present a hierarchy of SDP relaxations with asymptotic convergence for the FSIPP problem whose index set is defined by finitely many polynomial inequalities. Next, we study four cases of the FSIPP problems which can be reduced to either a single SDP problem or a finite sequence of SDP problems, where at least one minimizer can be extracted. Then, we apply this approach to the four corresponding multi-objective cases to find efficient solutions.
      PubDate: 2021-08-30
      DOI: 10.1007/s10589-021-00311-5
       
  • MADAM: a parallel exact solver for max-cut based on semidefinite
           programming and ADMM

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      Abstract: We present MADAM, a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.
      PubDate: 2021-08-26
      DOI: 10.1007/s10589-021-00310-6
       
 
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