Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)            First | 1 2 3 4 | Last

Showing 201 - 400 of 538 Journals sorted alphabetically
Educação Matemática Debate     Open Access  
Edumatica : Jurnal Pendidikan Matematika     Open Access  
EduMatSains     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 3)
Em Teia : Revista de Educação Matemática e Tecnológica Iberoamericana     Open Access  
Emergent Scientist     Open Access  
Energy for Sustainable Development     Hybrid Journal   (Followers: 13)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Open Access   (Followers: 2)
Euclid     Open Access  
European Journal of Applied Mathematics     Hybrid Journal  
European Journal of Combinatorics     Full-text available via subscription   (Followers: 3)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 1)
Examples and Counterexamples     Open Access  
Experimental Mathematics     Hybrid Journal   (Followers: 5)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Extracta Mathematicae     Open Access  
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 5)
Fixed Point Theory and Applications     Open Access  
Formalized Mathematics     Open Access  
Forum of Mathematics, Pi     Open Access   (Followers: 1)
Forum of Mathematics, Sigma     Open Access   (Followers: 1)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 6)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Stochastic Systems     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Theoretical Computer Science     Full-text available via subscription   (Followers: 1)
Foundations of Computational Mathematics     Hybrid Journal  
Fractal and Fractional     Open Access  
Fractals     Hybrid Journal   (Followers: 1)
Frontiers of Mathematics in China     Hybrid Journal  
Fuel Cells Bulletin     Full-text available via subscription   (Followers: 9)
Functional Analysis and Other Mathematics     Hybrid Journal   (Followers: 4)
Fundamental Journal of Mathematics and Applications     Open Access  
Funktsional'nyi Analiz i ego Prilozheniya     Full-text available via subscription  
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 8)
Game Theory     Open Access   (Followers: 2)
Games     Open Access   (Followers: 4)
Games and Economic Behavior     Hybrid Journal   (Followers: 25)
Gamm - Mitteilungen     Hybrid Journal  
GANIT : Journal of Bangladesh Mathematical Society     Open Access  
GEM - International Journal on Geomathematics     Hybrid Journal   (Followers: 1)
General Mathematics     Open Access  
Glasgow Mathematical Journal     Full-text available via subscription  
Global Journal of Mathematical Sciences     Full-text available via subscription  
Graphs and Combinatorics     Hybrid Journal   (Followers: 4)
Grey Systems : Theory and Application     Hybrid Journal  
Groups, Complexity, Cryptology     Open Access   (Followers: 2)
GSTF Journal of Mathematics, Statistics and Operations Research     Open Access   (Followers: 1)
Historia Mathematica     Full-text available via subscription  
Historical Methods: A Journal of Quantitative and Interdisciplinary History     Hybrid Journal   (Followers: 28)
IMA Journal of Applied Mathematics     Hybrid Journal  
IMA Journal of Numerical Analysis - advance access     Hybrid Journal  
ImmunoInformatics     Open Access   (Followers: 1)
Indagationes Mathematicae     Open Access  
Indian Journal of Pure and Applied Mathematics     Hybrid Journal   (Followers: 4)
Indonesian Journal of Combinatorics     Open Access  
Indonesian Journal of Science and Mathematics Education     Open Access   (Followers: 1)
Infinite Dimensional Analysis, Quantum Probability and Related Topics     Hybrid Journal   (Followers: 1)
Infinity Jurnal Matematika dan Aplikasinya     Open Access   (Followers: 3)
Information and Inference     Free  
InfoTekJar : Jurnal Nasional Informatika dan Teknologi Jaringan     Open Access  
InfraMatics     Open Access  
Insight - Non-Destructive Testing and Condition Monitoring     Full-text available via subscription   (Followers: 110)
International Electronic Journal of Algebra     Open Access  
International Journal for Numerical Methods in Engineering     Hybrid Journal   (Followers: 35)
International Journal for Numerical Methods in Fluids     Hybrid Journal   (Followers: 19)
International Journal of Advanced Mathematical Sciences     Open Access  
International Journal of Advanced Mechatronic Systems     Hybrid Journal   (Followers: 2)
International Journal of Advanced Research in Mathematics     Open Access  
International Journal of Advances in Engineering Sciences and Applied Mathematics     Hybrid Journal   (Followers: 10)
International Journal of Algebra and Computation     Hybrid Journal   (Followers: 1)
International Journal of Algebra and Statistics     Open Access   (Followers: 3)
International Journal of Applied and Computational Mathematics     Hybrid Journal  
International Journal of Applied Mathematical Research     Open Access   (Followers: 1)
International Journal of Applied Mathematics and Computer Science     Open Access   (Followers: 7)
International Journal of Applied Mechanics     Hybrid Journal   (Followers: 8)
International Journal of Applied Nonlinear Science     Hybrid Journal  
International Journal of Autonomic Computing     Hybrid Journal   (Followers: 1)
International Journal of Bifurcation and Chaos     Hybrid Journal   (Followers: 4)
International Journal of Biomathematics     Hybrid Journal   (Followers: 2)
International Journal of Computational Complexity and Intelligent Algorithms     Hybrid Journal  
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Computational Geometry and Applications     Hybrid Journal   (Followers: 2)
International Journal of Computational Intelligence and Applications     Hybrid Journal   (Followers: 2)
International Journal of Computational Methods     Hybrid Journal   (Followers: 4)
International Journal of Computer Processing Of Languages     Hybrid Journal   (Followers: 1)
International Journal of Control, Automation and Systems     Hybrid Journal   (Followers: 15)
International Journal of Dynamical Systems and Differential Equations     Hybrid Journal   (Followers: 1)
International Journal of Economics and Accounting     Hybrid Journal   (Followers: 1)
International Journal of Foundations of Computer Science     Hybrid Journal   (Followers: 3)
International Journal of Fuzzy Computation and Modelling     Hybrid Journal   (Followers: 2)
International Journal of Image and Graphics     Hybrid Journal   (Followers: 5)
International Journal of Industrial Electronics and Drives     Hybrid Journal   (Followers: 3)
International Journal of Low-Carbon Technologies     Open Access   (Followers: 1)
International Journal of Mathematical Education in Science and Technology     Hybrid Journal   (Followers: 9)
International Journal of Mathematical Modelling & Computations     Open Access   (Followers: 3)
International Journal of Mathematical Modelling and Numerical Optimisation     Hybrid Journal   (Followers: 5)
International Journal of Mathematical Sciences and Computing     Open Access  
International Journal of Mathematics     Hybrid Journal   (Followers: 4)
International Journal of Mathematics & Computation     Full-text available via subscription  
International Journal of Mathematics and Mathematical Sciences     Open Access   (Followers: 4)
International Journal of Mathematics in Operational Research     Hybrid Journal   (Followers: 2)
International Journal of Metaheuristics     Hybrid Journal   (Followers: 1)
International Journal of Modelling in Operations Management     Hybrid Journal   (Followers: 2)
International Journal of Modern Nonlinear Theory and Application     Open Access   (Followers: 1)
International Journal of Number Theory     Hybrid Journal   (Followers: 1)
International Journal of Partial Differential Equations     Open Access   (Followers: 2)
International Journal of Polymer Science     Open Access   (Followers: 25)
International Journal of Pure Mathematical Sciences     Open Access  
International Journal of Reliability, Quality and Safety Engineering     Hybrid Journal   (Followers: 14)
International Journal of Research in Undergraduate Mathematics Education     Hybrid Journal   (Followers: 4)
International Journal of Sediment Research     Full-text available via subscription   (Followers: 2)
International Journal of Shape Modeling     Hybrid Journal   (Followers: 1)
International Journal of Theoretical and Mathematical Physics     Open Access   (Followers: 13)
International Journal of Trends in Mathematics Education Research     Open Access   (Followers: 4)
International Journal of Ultra Wideband Communications and Systems     Hybrid Journal  
International Journal of Wavelets, Multiresolution and Information Processing     Hybrid Journal  
International Journal on Artificial Intelligence Tools     Hybrid Journal   (Followers: 9)
International Mathematics Research Notices     Hybrid Journal   (Followers: 1)
Internet Mathematics     Hybrid Journal   (Followers: 1)
Inventiones mathematicae     Hybrid Journal   (Followers: 2)
Inverse Problems in Science and Engineering     Hybrid Journal   (Followers: 3)
Investigations in Mathematics Learning     Hybrid Journal  
Iranian Journal of Optimization     Open Access   (Followers: 2)
Israel Journal of Mathematics     Hybrid Journal  
Ithaca : Viaggio nella Scienza     Open Access  
ITM Web of Conferences     Open Access  
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya     Full-text available via subscription  
Jahresbericht der Deutschen Mathematiker-Vereinigung     Hybrid Journal  
Japan Journal of Industrial and Applied Mathematics     Hybrid Journal  
Japanese Journal of Mathematics     Hybrid Journal  
JIPM (Jurnal Ilmiah Pendidikan Matematika)     Open Access  
JMPM : Jurnal Matematika dan Pendidikan Matematika     Open Access  
JOHME : Journal of Holistic Mathematics Education     Open Access   (Followers: 2)
Johnson Matthey Technology Review     Open Access  
Jornal Internacional de Estudos em Educação Matemática     Open Access  
Journal d'Analyse Mathématique     Hybrid Journal   (Followers: 2)
Journal de Mathématiques Pures et Appliquées     Full-text available via subscription   (Followers: 3)
Journal for Research in Mathematics Education     Full-text available via subscription   (Followers: 28)
Journal für Mathematik-Didaktik     Hybrid Journal  
Journal of Advanced Mathematics and Applications     Full-text available via subscription   (Followers: 1)
Journal of Algebra     Full-text available via subscription   (Followers: 3)
Journal of Algebra and Its Applications     Hybrid Journal   (Followers: 3)
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 3)
Journal of Algorithms & Computational Technology     Open Access  
Journal of Applied Mathematics     Open Access   (Followers: 3)
Journal of Applied Mathematics and Computing     Hybrid Journal  
Journal of Applied Mathematics, Statistics and Informatics     Open Access   (Followers: 1)
Journal of Artificial Intelligence and Data Mining     Open Access   (Followers: 10)
Journal of Classification     Hybrid Journal   (Followers: 5)
Journal of Combinatorial Designs     Hybrid Journal   (Followers: 4)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Combinatorial Theory, Series A     Full-text available via subscription   (Followers: 5)
Journal of Combinatorial Theory, Series B     Full-text available via subscription   (Followers: 3)
Journal of Complex Analysis     Open Access   (Followers: 2)
Journal of Complex Networks     Hybrid Journal   (Followers: 1)
Journal of Complexity     Hybrid Journal   (Followers: 6)
Journal of Computational and Applied Mathematics     Hybrid Journal   (Followers: 6)
Journal of Computational Biology     Hybrid Journal   (Followers: 9)
Journal of Computational Mathematics and Data Science     Open Access  
Journal of Computational Multiphase Flows     Open Access   (Followers: 1)
Journal of Computational Physics     Hybrid Journal   (Followers: 59)
Journal of Computational Physics : X     Open Access   (Followers: 1)
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 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  
Journal of Flood Risk Management     Hybrid Journal   (Followers: 14)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 3)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 4)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 6)
Journal of Global Research in Mathematical Archives     Open Access  
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  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 2)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal   (Followers: 1)
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 3)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 3)
Journal of mathematical and computational science     Open Access   (Followers: 2)

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Similar Journals
Journal Cover
Journal of Global Optimization
Journal Prestige (SJR): 1.311
Citation Impact (citeScore): 2
Number of Followers: 6  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2916 - ISSN (Online) 0925-5001
Published by Springer-Verlag Homepage  [2469 journals]
  • On convex lower-level black-box constraints in bilevel optimization with
           an application to gas market models with chance constraints

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      Abstract: Abstract Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.
      PubDate: 2022-05-13
       
  • On $$\Delta $$ Δ -modular integer linear problems in the canonical
           form and equivalent problems

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      Abstract: Abstract Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type \(\max \{c^\top x :A x = b,\, x \in {{\,\mathrm{\mathbb {Z}}\,}}^n_{\ge 0}\}\) , where all the entries of A, b, c are integer, parameterized by the number of rows of A and \(\Vert A\Vert _{\max }\) . This class of problems is known under the name of ILP problems in the standard form, adding the word ”bounded” if \(x \le u\) , for some integer vector u. Recently, many new sparsity, proximity, and complexity results were obtained for bounded and unbounded ILP problems in the standard form. In this paper, we consider ILP problems in the canonical form $$\begin{aligned} \max \{c^\top x :b_l \le A x \le b_r,\, x \in {{\,\mathrm{\mathbb {Z}}\,}}^n\}, \end{aligned}$$ where \(b_l\) and \(b_r\) are integer vectors. We assume that the integer matrix A has the rank n, \((n + m)\) rows, n columns, and parameterize the problem by m and \(\Delta (A)\) , where \(\Delta (A)\) is the maximum of \(n \times n\) sub-determinants of A, taken in the absolute value. We show that any ILP problem in the standard form can be polynomially reduced to some ILP problem in the canonical form, preserving m and \(\Delta (A)\) , but the reverse reduction is not always possible. More precisely, we define the class of generalized ILP problems in the standard form, which includes an additional group constraint, and prove the equivalence to ILP problems in the canonical form. We generalize known sparsity, proximity, and complexity bounds for ILP problems in the canonical form. Additionally, sometimes, we strengthen previously known results for ILP problems in the canonical form, and, sometimes, we give shorter proofs. Finally, we consider the special cases of \(m \in \{0,1\}\) . By this way, we give specialised sparsity, proximity, and complexity bounds for the problems on simplices, Knapsack problems and Subset-Sum problems.
      PubDate: 2022-05-10
       
  • Tight compact extended relaxations for nonconvex quadratic programming
           problems with box constraints

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      Abstract: Abstract Cutting planes from the Boolean Quadric Polytope can be used to reduce the optimality gap of the \(\mathcal {NP}\) -hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal–Gomory closure of the Boolean Quadric Polytope are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which allows to optimize over the Chvátal–Gomory closure without repeated calls to separation algorithms and has less inequalities than the formulation provided by Boros et al. (SIAM J Discrete Math 5(2):163–177, 1992) for sparse matrices. In a computational study, we confirm the strength of this relaxation and show that we can provide very strong bounds for the BoxQP, even with a plain linear program. The resulting bounds are significantly stronger than these from Bonami et al. (Math Program Comput 10(3):333–382, 2018), which arise from separating A-odd cycle inequalities heuristically.
      PubDate: 2022-05-09
       
  • Convergence rates for the heavy-ball continuous dynamics for non-convex
           optimization, under Polyak–Łojasiewicz condition

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      Abstract: Abstract We study convergence of the trajectories of the Heavy Ball dynamical system, with constant damping coefficient, in the framework of convex and non-convex smooth optimization. By using the Polyak–Łojasiewicz condition, we derive new linear convergence rates for the associated trajectory, in terms of objective function values, without assuming uniqueness of the minimizer.
      PubDate: 2022-05-06
       
  • Painlevé-Kuratowski convergence of minimal solutions for set-valued
           optimization problems via improvement sets

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      Abstract: Abstract The aim of this paper is to explore the stability of (weak)-minimal solutions for set-valued optimization problems via improvement sets. Firstly, the optimality and closedness of solution sets for the set-valued optimization problem under the upper order relation are discussed. Then, a new convergence concept for set-valued mapping sequences is introduced, and some properties of the set-valued mapping sequences are shown under the new convergence assumption. Moreover, by means of upper level sets, Painlevé-Kuratowski convergences of (weak) E-u-solutions to set-valued optimization problems with respect to the perturbations of feasible sets and objective mappings are established under mild conditions. The order that we use to establish the result depends on the improvement set, which is not necessarily a cone order. Our results can be seen as the extension of the related work established recently in this field.
      PubDate: 2022-05-03
       
  • Quasi-contingent derivatives and studies of higher-orders in nonsmooth
           optimization

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      Abstract: Abstract We consider higher-order conditions and sensitivity analysis for solutions to equilibrium problems. The conditions for solutions are in terms of quasi-contingent derivatives and involve higher-order complementarity slackness for both the objective and the constraints and under Hölder metric subregularity assumptions. For sensitivity analysis, a formula of this type of derivative of the solution map to a parametric equilibrium problem is established in terms of the same types of derivatives of the data of the problem. Here, the concepts of a quasi-contingent derivative and critical directions are new. We consider open-cone solutions and proper solutions. We also study an important and typical special case: weak solutions of a vector minimization problem with mixed constraints. The results are significantly new and improve recent corresponding results in many aspects.
      PubDate: 2022-05-03
       
  • Preface: special issue on optimization in distance geometry

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      PubDate: 2022-05-01
       
  • Mixed integer nonlinear optimization models for the Euclidean Steiner tree
           problem in $$\mathbb {R}^d$$ R d

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      Abstract: Abstract New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with \(d\ge 3\) ) will be presented in this work. All models feature a nonsmooth objective function but the continuous relaxations of their set of feasible solutions are convex. From these models, four convex mixed integer linear and nonlinear relaxations will be considered. Each relaxation has the same set of feasible solutions as the set of feasible solutions of the model from which it is derived. Finally, preliminary computational results highlighting the main features of the presented relaxations will be discussed.
      PubDate: 2022-05-01
       
  • NMR assignment through linear programming

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      Abstract: Abstract Nuclear Magnetic Resonance (NMR) Spectroscopy is the second most used technique (after X-ray crystallography) for structural determination of proteins. A computational challenge in this technique involves solving a discrete optimization problem that assigns the resonance frequency to each atom in the protein. This paper introduces LIAN (LInear programming Assignment for NMR), a novel linear programming formulation of the problem which yields state-of-the-art results in simulated and experimental datasets.
      PubDate: 2022-05-01
       
  • Unassigned distance geometry and molecular conformation problems

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      Abstract: Abstract 3D protein structures and nanostructures can be obtained by exploiting distance information provided by experimental techniques, such as nuclear magnetic resonance and the pair distribution function method. These are examples of instances of the unassigned distance geometry problem (uDGP), where the aim is to calculate the position of some points using a list of associated distance values not previoulsy assigned to the pair of points. We propose new mathematical programming formulations and a new heuristic to solve the uDGP related to molecular structure calculations. In addition to theoretical results, computational experiments are also provided.
      PubDate: 2022-05-01
       
  • Global exact optimization for covering a rectangle with 6 circles

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      Abstract: Abstract We address the problem of covering a rectangle with six identical circles, whose radius is to be minimized. We focus on open cases from Melissen and Schuur (Discrete Appl Math 99:149–156, 2000). Depending on the rectangle side lengths, different configurations of the circles, corresponding to the different ways they are placed, yield the optimal covering. We prove the optimality of the two configurations corresponding to open cases. For the first one, we propose a mathematical mixed-integer nonlinear optimization formulation, that allows one to compute global optimal solutions. For the second one, we provide an analytical expression of the optimal radius as a function of one of the rectangle side lengths. All open cases are thus closed for the optimal covering of a rectangle with six circles.
      PubDate: 2022-05-01
       
  • Side-constrained minimum sum-of-squares clustering: mathematical
           programming and random projections

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      Abstract: Abstract This paper investigates a mathematical programming based methodology for solving the minimum sum-of-squares clustering problem, also known as the “k-means problem”, in the presence of side constraints. We propose several exact and approximate mixed-integer linear and nonlinear formulations. The approximations are based on norm inequalities and random projections, the approximation guarantees of which are based on an additive version of the Johnson–Lindenstrauss lemma. We perform computational testing (with fixed CPU time) on a range of randomly generated and real data instances of medium size, but with high dimensionality. We show that when side constraints make k-means inapplicable, our proposed methodology—which is easy and fast to implement and deploy—can obtain good solutions in limited amounts of time.
      PubDate: 2022-05-01
       
  • An exact algorithm for constructing minimum Euclidean skeletons of
           polygons

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      Abstract: Abstract A Euclidean skeleton is a set of edges in the interior (or on the boundary) of a polygon that intersects any line segment that joins two points outside of the polygon and that intersects the polygon. In this paper we study minimum cardinality Euclidean skeletons and develop an algorithm for constructing them. We first prove a number of structural properties of minimum skeletons and use these to develop a canonical form. We then design an exact algorithm which initially generates a set of canonical skeleton edges, then executes a pruning module to reduce the set of candidate edges, and finally runs existing integer linear programming code to output an optimal solution. Finally, we perform computational testing on our algorithm to demonstrate its performance, and observe a number of experimental properties of minimum skeletons.
      PubDate: 2022-05-01
       
  • Maximum feasible subsystems of distance geometry constraints

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      Abstract: Abstract We study the problem of satisfying the maximum number of distance geometry constraints with minimum experimental error. This models the determination of the shape of proteins from atomic distance data which are obtained from nuclear magnetic resonance experiments and exhibit experimental and systematic errors. Experimental errors are represented by interval constraints on Euclidean distances. Systematic errors occur from a misassignment of distances to wrong atomic pairs: we represent such errors by maximizing the number of satisfiable distance constraints. We present many mathematical programming formulations, as well as a “matheuristic” algorithm based on reformulations, relaxations, restrictions and refinement. We show that this algorithm works on protein graphs with hundreds of atoms and thousands of distances.
      PubDate: 2022-05-01
       
  • Which graphs are rigid in $$\ell _p^d$$ ℓ p d '

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      Abstract: Abstract We present three results which support the conjecture that a graph is minimally rigid in d-dimensional \(\ell _p\) -space, where \(p\in (1,\infty )\) and \(p\not =2\) , if and only if it is (d, d)-tight. Firstly, we introduce a graph bracing operation which preserves independence in the generic rigidity matroid when passing from \(\ell _p^d\) to \(\ell _p^{d+1}\) . We then prove that every (d, d)-sparse graph with minimum degree at most \(d+1\) and maximum degree at most \(d+2\) is independent in \(\ell _p^d\) . Finally, we prove that every triangulation of the projective plane is minimally rigid in \(\ell _p^3\) . A catalogue of rigidity preserving graph moves is also provided for the more general class of strictly convex and smooth normed spaces and we show that every triangulation of the sphere is independent for 3-dimensional spaces in this class.
      PubDate: 2022-05-01
       
  • Parallel algorithm portfolios with adaptive resource allocation strategy

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      Abstract: Abstract Algorithm portfolios are multi-algorithmic schemes that combine a number of solvers into a joint framework for solving global optimization problems. A crucial part of such schemes is the resource allocation process that is responsible for assigning computational resources to the constituent algorithms. We propose a resource allocation process based on adaptive decision-making procedures. The proposed approach is incorporated in algorithm portfolios composed of three essential types of numerical optimization algorithms, namely gradient-based, direct search, and swarm intelligence algorithms. The designed algorithm portfolios are experimentally demonstrated on a challenging optimization problem for different dimensions and experimental settings. The accompanying statistical analysis offers interesting conclusions and insights on the performance of the algorithm portfolio compared to its constituent algorithms, as well as on the effect of its parameters.
      PubDate: 2022-04-30
       
  • A novel update rule of HALS algorithm for nonnegative matrix factorization
           and Zangwill’s global convergence

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      Abstract: Abstract Nonnegative Matrix Factorization (NMF) has attracted a great deal of attention as an effective technique for dimensionality reduction of large-scale nonnegative data. Given a nonnegative matrix, NMF aims to obtain two low-rank nonnegative factor matrices by solving a constrained optimization problem. The Hierarchical Alternating Least Squares (HALS) algorithm is a well-known and widely-used iterative method for solving such optimization problems. However, the original update rule used in the HALS algorithm is not well defined. In this paper, we propose a novel well-defined update rule of the HALS algorithm, and prove its global convergence in the sense of Zangwill. Unlike conventional globally-convergent update rules, the proposed one allows variables to take the value of zero and hence can obtain sparse factor matrices. We also present two stopping conditions that guarantee the finite termination of the HALS algorithm. The practical usefulness of the proposed update rule is shown through experiments using real-world datasets.
      PubDate: 2022-04-30
       
  • Zeroth-order algorithms for nonconvex–strongly-concave minimax problems
           with improved complexities

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      Abstract: Abstract In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a deterministic version of the problem. We design and analyze the Zeroth-Order Gradient Descent Ascent (ZO-GDA) algorithm, and provide improved results compared to existing works, in terms of oracle complexity. We also propose the Zeroth-Order Gradient Descent Multi-Step Ascent (ZO-GDMSA) algorithm that significantly improves the oracle complexity of ZO-GDA. We then consider stochastic versions of ZO-GDA and ZO-GDMSA, to handle stochastic nonconvex minimax problems. For this case, we provide oracle complexity results under two assumptions on the stochastic gradient: (i) the uniformly bounded variance assumption, which is common in traditional stochastic optimization, and (ii) the Strong Growth Condition (SGC), which has been known to be satisfied by modern over-parameterized machine learning models. We establish that under the SGC assumption, the complexities of the stochastic algorithms match that of deterministic algorithms. Numerical experiments are presented to support our theoretical results.
      PubDate: 2022-04-29
       
  • On complexity and convergence of high-order coordinate descent algorithms
           for smooth nonconvex box-constrained minimization

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      Abstract: Abstract Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models for smooth nonconvex box-constrained minimization are introduced in this work. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order \(\varepsilon \) -stationarity with respect to the variables of each coordinate-descent block is \(O(\varepsilon ^{-(p+1)/p})\) whereas the computer work for getting first-order \(\varepsilon \) -stationarity with respect to all the variables simultaneously is \(O(\varepsilon ^{-(p+1)})\) . Numerical examples involving multidimensional scaling problems are presented. The numerical performance of the methods is enhanced by means of coordinate-descent strategies for choosing initial points.
      PubDate: 2022-04-28
       
  • Scalar and vector equilibrium problems with pairs of bifunctions

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      Abstract: Abstract In this paper, existence results for scalar and vector equilibrium problems involving two bifunctions are established. To this aim, a new concept of generalized pseudomonotonicity for a pair of bifunctions is introduced. It leads to existence criteria different from the ones encountered in the literature. The given applications refer to minimax inequalities and variational inequality problems.
      PubDate: 2022-04-26
       
 
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