Subjects -> MATHEMATICS (Total: 1119 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (822 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (25 journals)

MATHEMATICS (822 journals)            First | 1 2 3 4 5     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 5)
Journal of Difference Equations and Applications     Hybrid Journal  
Journal of Differential Equations     Full-text available via subscription   (Followers: 1)
Journal of Discrete Algorithms     Hybrid Journal   (Followers: 4)
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 14)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 3)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 5)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 3)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 9)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 3)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 10)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Mathematics and Statistics Studies     Open Access   (Followers: 3)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 3)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 8)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access   (Followers: 1)
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 5)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
Journal of Progressive Research in Mathematics     Open Access   (Followers: 5)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 9)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 16)
Journal of Turbulence     Hybrid Journal   (Followers: 9)
Journal of Uncertainty Analysis and Applications     Open Access   (Followers: 1)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 6)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 2)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access   (Followers: 3)
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 6)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 3)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 23)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal   (Followers: 1)
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Models in Engineering     Open Access   (Followers: 1)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 4)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 2)
Mathematics Education Journal     Open Access   (Followers: 3)
Mathematics Education Research Journal     Partially Free   (Followers: 20)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 6)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MathLAB Journal     Open Access   (Followers: 5)
MATICS     Open Access   (Followers: 2)
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal  
Metascience     Hybrid Journal   (Followers: 1)
Metrology and Instruments / Метрологія та прилади     Open Access  
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal   (Followers: 5)
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 2)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal   (Followers: 1)
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)
North Carolina Journal of Mathematics and Statistics     Open Access  
North-Holland Mathematical Library     Full-text available via subscription   (Followers: 1)
North-Holland Mathematics Studies     Full-text available via subscription  

  First | 1 2 3 4 5     

Similar Journals
Journal Cover
Mathematical Programming Computation
Journal Prestige (SJR): 1.293
Citation Impact (citeScore): 3
Number of Followers: 3  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1867-2957 - ISSN (Online) 1867-2949
Published by Springer-Verlag Homepage  [2656 journals]
  • Solving equilibrium problems using extended mathematical programming
    • Abstract: We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set of constructs with which users annotate variables and equations of the model to describe equilibrium and variational problems. Our constructs enable a natural translation of the model from one formulation to another more computationally tractable form without requiring the modeler to supply derivatives. In the context of many independent agents in the equilibrium, we facilitate expression of sophisticated structures such as shared constraints and additional constraints on their solutions. We define shared variables and demonstrate their uses for sparse reformulation, economic equilibrium problems sharing economic states, mixed pricing behavior of agents, and so on. We give some equilibrium and variational examples from the literature and describe how to formulate them using our framework. Experimental results comparing performance of various complementarity formulations for shared variables are provided. Our framework has been implemented and is available within GAMS/EMP.
      PubDate: 2019-03-02
      DOI: 10.1007/s12532-019-00156-4
  • CasADi: a software framework for nonlinear optimization and optimal
    • Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.
      PubDate: 2019-03-01
      DOI: 10.1007/s12532-018-0139-4
  • A computational comparison of symmetry handling methods for mixed integer
    • Abstract: The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received significant attention, both in theory and practice. This paper compares different methods for handling symmetries using a common implementation framework. We start by investigating the computation of symmetries and analyze the symmetries present in the MIPLIB 2010 instances. It turns out that many instances are affected by symmetry and most symmetry groups contain full symmetric groups as factors. We then present (variants of) six symmetry handling methods from the literature. Their implementation is tested on several testsets. On very symmetric instances used previously in the literature, it is essential to use methods like isomorphism pruning, orbital fixing, or orbital branching. Moreover, tests on the MIPLIB instances show that isomorphism pruning, orbital fixing, or adding symmetry breaking inequalities allow to speed-up the solution process by about 15% and more instances can be solved within the time limit.
      PubDate: 2019-03-01
      DOI: 10.1007/s12532-018-0140-y
  • New global algorithms for quadratic programming with a few negative
           eigenvalues based on alternative direction method and convex relaxation
    • Abstract: We consider a quadratic program with a few negative eigenvalues (QP-r-NE) subject to linear and convex quadratic constraints that covers many applications and is known to be NP-hard even with one negative eigenvalue (QP1NE). In this paper, we first introduce a new global algorithm (ADMBB), which integrates several simple optimization techniques such as alternative direction method, and branch-and-bound, to find a globally optimal solution to the underlying QP within a pre-specified \(\epsilon \) -tolerance. We establish the convergence of the ADMBB algorithm and estimate its complexity. Second, we develop a global search algorithm (GSA) for QP1NE that can locate an optimal solution to QP1NE within \(\epsilon \) -tolerance and estimate the worst-case complexity bound of the GSA. Preliminary numerical results demonstrate that the ADMBB algorithm can effectively find a global optimal solution to large-scale QP-r-NE instances when \(r\le 10\) , and the GSA outperforms the ADMBB for most of the tested QP1NE instances. The software reviewed as part of this submission was given the
      DOI (digital object identifier)
      PubDate: 2019-03-01
  • Computing feasible points for binary MINLPs with MPECs
    • Abstract: Nonconvex mixed-binary nonlinear optimization problems frequently appear in practice and are typically extremely hard to solve. In this paper we discuss a class of primal heuristics that are based on a reformulation of the problem as a mathematical program with equilibrium constraints. We then use different regularization schemes for this class of problems and use an iterative solution procedure for solving series of regularized problems. In the case of success, these procedures result in a feasible solution of the original mixed-binary nonlinear problem. Since we rely on local nonlinear programming solvers the resulting method is fast and we further improve its reliability by additional algorithmic techniques. We show the strength of our method by an extensive computational study on 662 MINLPLib2instances, where our methods are able to produce feasible solutions for \({60}{\%}\) of all instances in at most \({10}\,{\hbox {s}}\) .
      PubDate: 2019-03-01
      DOI: 10.1007/s12532-018-0141-x
  • Enumeration of 2-level polytopes
    • Abstract: A (convex) polytope P is said to be 2-level if for each hyperplane H that supports a facet of P, the vertices of P can be covered with H and exactly one other translate of H. The study of these polytopes is motivated by questions in combinatorial optimization and communication complexity, among others. In this paper, we present the first algorithm for enumerating all combinatorial types of 2-level polytopes of a given dimension d, and provide complete experimental results for \(d \leqslant 7\) . Our approach is inductive: for each fixed \((d-1)\) -dimensional 2-level polytope \(P_0\) , we enumerate all d-dimensional 2-level polytopes P that have \(P_0\) as a facet. This relies on the enumeration of the closed sets of a closure operator over a finite ground set. By varying the prescribed facet \(P_0\) , we obtain all 2-level polytopes in dimension d.
      PubDate: 2019-03-01
      DOI: 10.1007/s12532-018-0145-6
  • Solving quadratic programs to high precision using scaled iterative
    • Abstract: Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library.
      PubDate: 2019-02-06
      DOI: 10.1007/s12532-019-00154-6
  • Certifiably optimal sparse principal component analysis
    • Abstract: This paper addresses the sparse principal component analysis (SPCA) problem for covariance matrices in dimension n aiming to find solutions with sparsity k using mixed integer optimization. We propose a tailored branch-and-bound algorithm, Optimal-SPCA, that enables us to solve SPCA to certifiable optimality in seconds for \(n = 100\)  s, \(k=10\)  s. This same algorithm can be applied to problems with \(n=10{,}000\,\mathrm{s}\) or higher to find high-quality feasible solutions in seconds while taking several hours to prove optimality. We apply our methods to a number of real data sets to demonstrate that our approach scales to the same problem sizes attempted by other methods, while providing superior solutions compared to those methods, explaining a higher portion of variance and permitting complete control over the desired sparsity. The software that was reviewed as part of this submission has been given the
      DOI (digital object identifier)
      PubDate: 2019-01-01
  • Simplex QP-based methods for minimizing a conic quadratic objective over
    • Abstract: We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be solved by polynomial interior point algorithms for conic quadratic optimization. However, interior point algorithms are not well-suited for branch-and-bound algorithms for the discrete counterparts of these problems due to the lack of effective warm starts necessary for the efficient solution of convex relaxations repeatedly at the nodes of the search tree. In order to overcome this shortcoming, we reformulate the problem using the perspective of the quadratic function. The perspective reformulation lends itself to simple coordinate descent and bisection algorithms utilizing the simplex method for quadratic programming, which makes the solution methods amenable to warm starts and suitable for branch-and-bound algorithms. We test the simplex-based quadratic programming algorithms to solve convex as well as discrete instances and compare them with the state-of-the-art approaches. The computational experiments indicate that the proposed algorithms scale much better than interior point algorithms and return higher precision solutions. In our experiments, for large convex instances, they provide up to 22x speed-up. For smaller discrete instances, the speed-up is about 13x over a barrier-based branch-and-bound algorithm and 6x over the LP-based branch-and-bound algorithm with extended formulations. The software that was reviewed as part of this submission was given the Digital Object identifier
      PubDate: 2018-12-03
      DOI: 10.1007/s12532-018-0152-7
  • Matrix minor reformulation and SOCP-based spatial branch-and-cut method
           for the AC optimal power flow problem
    • Abstract: Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major computational challenge to today’s power industry for the real-time operation of large-scale power grids. In this paper, we propose a new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable and characterize all such minors into three types. We show the equivalence of these minor constraints to the physical constraints of voltage angle differences summing to zero over three- and four-cycles in the power network. We study second-order conic programming (SOCP) relaxations of this minor reformulation and propose strong cutting planes, convex envelopes, and bound tightening techniques to strengthen the resulting SOCP relaxations. We then propose an SOCP-based spatial branch-and-cut method to obtain the global optimum of AC OPF. Extensive computational experiments show that the proposed algorithm significantly outperforms the state-of-the-art SDP-based OPF solver and on a simple personal computer is able to obtain on average a \(0.71\%\) optimality gap in no more than 720 s for the most challenging power system instances in the literature.
      PubDate: 2018-12-01
      DOI: 10.1007/s12532-018-0150-9
  • RBFOpt: an open-source library for black-box optimization with costly
           function evaluations
    • Abstract: We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the solution methodology implemented in the open-source library RBFOpt, available on COIN-OR. The algorithm is based on the Radial Basis Function method originally proposed by Gutmann (J Glob Optim 19:201–227, 2001., which builds and iteratively refines a surrogate model of the unknown objective function. The two main methodological contributions of this paper are an approach to exploit a noisy but less expensive oracle to accelerate convergence to the optimum of the exact oracle, and the introduction of an automatic model selection phase during the optimization process. Numerical experiments show that RBFOpt is highly competitive on a test set of continuous and mixed-integer nonlinear unconstrained problems taken from the literature: it outperforms the open-source solvers included in our comparison by a large amount, and performs slightly better than a commercial solver. Our empirical evaluation provides insight on which parameterizations of the algorithm are the most effective in practice. The software reviewed as part of this submission was given the Digital Object Identifier (
      DOI )
      PubDate: 2018-12-01
  • ADMM for the SDP relaxation of the QAP
    • Abstract: Semidefinite programming, SDP, relaxations have proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem, QAP, arguably one of the hardest NP-hard discrete optimization problems. There are several difficulties that arise in efficiently solving the SDP relaxation, e.g., increased dimension; inefficiency of the current primal–dual interior point solvers in terms of both time and accuracy; and difficulty and high expense in adding cutting plane constraints. We propose using the alternating direction method of multipliers ADMM in combination with facial reduction, FR, to solve the SDP relaxation. This first order approach allows for: inexpensive iterations, a method of cheaply obtaining low rank solutions; and a trivial way of exploiting the FR for adding cutting plane inequalities. In fact, we solve the doubly nonnegative, DNN, relaxation that includes both the SDP and all the nonnegativity constraints. When compared to current approaches and current best available bounds we obtain robustness, efficiency and improved bounds.
      PubDate: 2018-12-01
      DOI: 10.1007/s12532-018-0148-3
  • Learning customized and optimized lists of rules with mathematical
    • Abstract: We introduce a mathematical programming approach to building rule lists, which are a type of interpretable, nonlinear, and logical machine learning classifier involving IF-THEN rules. Unlike traditional decision tree algorithms like CART and C5.0, this method does not use greedy splitting and pruning. Instead, it aims to fully optimize a combination of accuracy and sparsity, obeying user-defined constraints. This method is useful for producing non-black-box predictive models, and has the benefit of a clear user-defined tradeoff between training accuracy and sparsity. The flexible framework of mathematical programming allows users to create customized models with a provable guarantee of optimality. The software reviewed as part of this submission was given the
      DOI (Digital Object Identifier)
      PubDate: 2018-12-01
  • Optimizing over pure stationary equilibria in consensus stopping games
    • Abstract: Consensus decision-making, a widely utilized group decision-making process, requires the consent of all participants. We consider consensus stopping games, a class of stochastic games arising in the context of consensus decision-making that require the consent of all players to terminate the game. We show that a consensus stopping game may have many pure stationary equilibria, which in turn raises the question of equilibrium selection. Given an objective criterion, we study the NP-hard problem of finding a best pure stationary equilibrium. We characterize the pure stationary equilibria, show that they form an independence system, and develop several families of valid inequalities. We then solve the equilibrium selection problem as a mixed-integer linear program by a branch-and-cut approach. Our computational results demonstrate the effectiveness of our approach over a commercial solver.
      PubDate: 2018-11-02
      DOI: 10.1007/s12532-018-0151-8
  • Solving linear programs with complementarity constraints using
    • Abstract: A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium constraints. The presence of the complementarity constraints results in a nonconvex optimization problem. We develop a branch-and-cut algorithm to find a global optimum for this class of optimization problems, where we branch directly on complementarities. We develop branching rules and feasibility recovery procedures and demonstrate their computational effectiveness in a comparison with CPLEX. The implementation builds on CPLEX through the use of callback routines. The computational results show that our approach is a strong alternative to constructing an integer programming formulation using big-M terms to represent bounds for variables, with testing conducted on general LPCCs as well as on instances generated from bilevel programs with convex quadratic lower level problems.
      PubDate: 2018-09-27
      DOI: 10.1007/s12532-018-0149-2
  • QPLIB: a library of quadratic programming instances
    • Abstract: This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the variety of QP solution methods, ranging from entirely combinatorial approaches to completely continuous algorithms, including many methods for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the different, interested communities is therefore important. We propose a simple taxonomy for QP instances leading to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.
      PubDate: 2018-09-22
      DOI: 10.1007/s12532-018-0147-4
  • QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic
           semidefinite programming
    • Authors: Xudong Li; Defeng Sun; Kim-Chuan Toh
      Abstract: In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality and inequality constraints, a simple convex polyhedral set constraint, and a positive semidefinite cone constraint. A first order algorithm which relies on the inexact Schur complement based decomposition technique is developed in QSDPNAL-Phase I with the aim of solving a QSDP problem to moderate accuracy or using it to generate a reasonably good initial point for the second phase. In QSDPNAL-Phase II, we design an augmented Lagrangian method (ALM) wherein the inner subproblem in each iteration is solved via inexact semismooth Newton based algorithms. Simple and implementable stopping criteria are designed for the ALM. Moreover, under mild conditions, we are able to establish the rate of convergence of the proposed algorithm and prove the R-(super)linear convergence of the KKT residual. In the implementation of QSDPNAL, we also develop efficient techniques for solving large scale linear systems of equations under certain subspace constraints. More specifically, simpler and yet better conditioned linear systems are carefully designed to replace the original linear systems and novel shadow sequences are constructed to alleviate the numerical difficulties brought about by the crucial subspace constraints. Extensive numerical results for various large scale QSDPs show that our two-phase algorithm is highly efficient and robust in obtaining accurate solutions. The software reviewed as part of this submission was given the
      DOI (Digital Object Identifier)
      PubDate: 2018-04-13
  • The GeoSteiner software package for computing Steiner trees in the plane:
           an updated computational study
    • Authors: Daniel Juhl; David M. Warme; Pawel Winter; Martin Zachariasen
      Abstract: The GeoSteiner software package has for about 20 years been the fastest (publicly available) program for computing exact solutions to Steiner tree problems in the plane. The computational study by Warme, Winter and Zachariasen, published in 2000, documented the performance of the GeoSteiner approach—allowing the exact solution of Steiner tree problems with more than a thousand terminals. Since then, a number of algorithmic enhancements have improved the performance of the software package significantly. We describe these (previously unpublished) enhancements, and present a new computational study wherein we run the current code on the largest problem instances from the 2000-study, and on a number of larger problem instances. The computational study is performed using the commercial GeoSteiner 4.0 code base, and the performance is compared to the publicly available GeoSteiner 3.1 code base as well as the code base from the 2000-study. The software studied in the paper is being released as GeoSteiner 5.0 under an open source license.
      PubDate: 2018-02-20
      DOI: 10.1007/s12532-018-0135-8
  • Cubic regularization in symmetric rank-1 quasi-Newton methods
    • Authors: Hande Y. Benson; David F. Shanno
      Abstract: Quasi-Newton methods based on the symmetric rank-one (SR1) update have been known to be fast and provide better approximations of the true Hessian than popular rank-two approaches, but these properties are guaranteed under certain conditions which frequently do not hold. Additionally, SR1 is plagued by the lack of guarantee of positive definiteness for the Hessian estimate. In this paper, we propose cubic regularization as a remedy to relax the conditions on the proofs of convergence for both speed and accuracy and to provide a positive definite approximation at each step. We show that the n-step convergence property for strictly convex quadratic programs is retained by the proposed approach. Extensive numerical results on unconstrained problems from the CUTEr test set are provided to demonstrate the computational efficiency and robustness of the approach.
      PubDate: 2018-02-12
      DOI: 10.1007/s12532-018-0136-7
  • A generalized alternating direction method of multipliers with
           semi-proximal terms for convex composite conic programming
    • Authors: Yunhai Xiao; Liang Chen; Donghui Li
      Abstract: In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate accuracy. Our primary motivation is that this method, together with properly chosen semi-proximal terms, such as those generated by the recent advance of block symmetric Gauss–Seidel technique, is capable of tackling these problems. Moreover, the proposed method, which relaxes both the primal and the dual variables in a natural way with a common relaxation factor in the interval of (0, 2), has the potential of enhancing the performance of the classic ADMM. Extensive numerical experiments on various doubly non-negative semidefinite programming problems, with or without inequality constraints, are conducted. The corresponding results showed that all these multi-block problems can be successively solved, and the advantage of using the relaxation step is apparent.
      PubDate: 2018-01-23
      DOI: 10.1007/s12532-018-0134-9
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