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  Subjects -> STATISTICS (Total: 130 journals)
Showing 1 - 151 of 151 Journals sorted alphabetically
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 61)
Annals of Applied Statistics     Full-text available via subscription   (Followers: 39)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Argumentation et analyse du discours     Open Access   (Followers: 10)
Asian Journal of Mathematics & Statistics     Open Access   (Followers: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 4)
Australian & New Zealand Journal of Statistics     Hybrid Journal   (Followers: 13)
Bernoulli     Full-text available via subscription   (Followers: 9)
Biometrical Journal     Hybrid Journal   (Followers: 10)
Biometrics     Hybrid Journal   (Followers: 51)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Building Simulation     Hybrid Journal   (Followers: 1)
Bulletin of Statistics     Full-text available via subscription   (Followers: 4)
CHANCE     Hybrid Journal   (Followers: 5)
Communications in Statistics - Simulation and Computation     Hybrid Journal   (Followers: 9)
Communications in Statistics - Theory and Methods     Hybrid Journal   (Followers: 11)
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 37)
Current Research in Biostatistics     Open Access   (Followers: 8)
Decisions in Economics and Finance     Hybrid Journal   (Followers: 11)
Demographic Research     Open Access   (Followers: 16)
Electronic Journal of Statistics     Open Access   (Followers: 8)
Engineering With Computers     Hybrid Journal   (Followers: 5)
Environmental and Ecological Statistics     Hybrid Journal   (Followers: 7)
ESAIM: Probability and Statistics     Full-text available via subscription   (Followers: 5)
Extremes     Hybrid Journal   (Followers: 2)
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 8)
Geneva Papers on Risk and Insurance - Issues and Practice     Hybrid Journal   (Followers: 13)
Handbook of Numerical Analysis     Full-text available via subscription   (Followers: 5)
Handbook of Statistics     Full-text available via subscription   (Followers: 7)
IEA World Energy Statistics and Balances -     Full-text available via subscription   (Followers: 2)
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Quality, Statistics, and Reliability     Open Access   (Followers: 17)
International Journal of Stochastic Analysis     Open Access   (Followers: 3)
International Statistical Review     Hybrid Journal   (Followers: 12)
International Trade by Commodity Statistics - Statistiques du commerce international par produit     Full-text available via subscription  
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 4)
Journal of Applied Statistics     Hybrid Journal   (Followers: 20)
Journal of Biopharmaceutical Statistics     Hybrid Journal   (Followers: 20)
Journal of Business & Economic Statistics     Full-text available via subscription   (Followers: 39, SJR: 3.664, CiteScore: 2)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Computational & Graphical Statistics     Full-text available via subscription   (Followers: 20)
Journal of Econometrics     Hybrid Journal   (Followers: 82)
Journal of Educational and Behavioral Statistics     Hybrid Journal   (Followers: 6)
Journal of Forecasting     Hybrid Journal   (Followers: 17)
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Interactive Marketing     Hybrid Journal   (Followers: 10)
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Nonparametric Statistics     Hybrid Journal   (Followers: 6)
Journal of Probability and Statistics     Open Access   (Followers: 10)
Journal of Risk and Uncertainty     Hybrid Journal   (Followers: 32)
Journal of Statistical and Econometric Methods     Open Access   (Followers: 5)
Journal of Statistical Physics     Hybrid Journal   (Followers: 13)
Journal of Statistical Planning and Inference     Hybrid Journal   (Followers: 8)
Journal of Statistical Software     Open Access   (Followers: 20, SJR: 13.802, CiteScore: 16)
Journal of the American Statistical Association     Full-text available via subscription   (Followers: 72, SJR: 3.746, CiteScore: 2)
Journal of the Korean Statistical Society     Hybrid Journal   (Followers: 1)
Journal of the Royal Statistical Society Series C (Applied Statistics)     Hybrid Journal   (Followers: 31)
Journal of the Royal Statistical Society, Series A (Statistics in Society)     Hybrid Journal   (Followers: 26)
Journal of the Royal Statistical Society, Series B (Statistical Methodology)     Hybrid Journal   (Followers: 43)
Journal of Theoretical Probability     Hybrid Journal   (Followers: 3)
Journal of Time Series Analysis     Hybrid Journal   (Followers: 16)
Journal of Urbanism: International Research on Placemaking and Urban Sustainability     Hybrid Journal   (Followers: 30)
Law, Probability and Risk     Hybrid Journal   (Followers: 8)
Lifetime Data Analysis     Hybrid Journal   (Followers: 7)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Measurement Interdisciplinary Research and Perspectives     Hybrid Journal   (Followers: 1)
Metrika     Hybrid Journal   (Followers: 4)
Modelling of Mechanical Systems     Full-text available via subscription   (Followers: 1)
Monte Carlo Methods and Applications     Hybrid Journal   (Followers: 6)
Monthly Statistics of International Trade - Statistiques mensuelles du commerce international     Full-text available via subscription   (Followers: 2)
Multivariate Behavioral Research     Hybrid Journal   (Followers: 5)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 8)
Oxford Bulletin of Economics and Statistics     Hybrid Journal   (Followers: 34)
Pharmaceutical Statistics     Hybrid Journal   (Followers: 17)
Probability Surveys     Open Access   (Followers: 4)
Queueing Systems     Hybrid Journal   (Followers: 7)
Research Synthesis Methods     Hybrid Journal   (Followers: 7)
Review of Economics and Statistics     Hybrid Journal   (Followers: 124)
Review of Socionetwork Strategies     Hybrid Journal  
Risk Management     Hybrid Journal   (Followers: 15)
Sankhya A     Hybrid Journal   (Followers: 2)
Scandinavian Journal of Statistics     Hybrid Journal   (Followers: 9)
Sequential Analysis: Design Methods and Applications     Hybrid Journal  
Significance     Hybrid Journal   (Followers: 7)
Sociological Methods & Research     Hybrid Journal   (Followers: 37)
SourceOCDE Comptes nationaux et Statistiques retrospectives     Full-text available via subscription  
SourceOCDE Statistiques : Sources et methodes     Full-text available via subscription  
SourceOECD Bank Profitability Statistics - SourceOCDE Rentabilite des banques     Full-text available via subscription   (Followers: 1)
SourceOECD Insurance Statistics - SourceOCDE Statistiques d'assurance     Full-text available via subscription   (Followers: 2)
SourceOECD Main Economic Indicators - SourceOCDE Principaux indicateurs economiques     Full-text available via subscription   (Followers: 1)
SourceOECD Measuring Globalisation Statistics - SourceOCDE Mesurer la mondialisation - Base de donnees statistiques     Full-text available via subscription  
SourceOECD Monthly Statistics of International Trade     Full-text available via subscription   (Followers: 1)
SourceOECD National Accounts & Historical Statistics     Full-text available via subscription  
SourceOECD OECD Economic Outlook Database - SourceOCDE Statistiques des Perspectives economiques de l'OCDE     Full-text available via subscription   (Followers: 2)
SourceOECD Science and Technology Statistics - SourceOCDE Base de donnees des sciences et de la technologie     Full-text available via subscription  
SourceOECD Statistics Sources & Methods     Full-text available via subscription   (Followers: 1)
SourceOECD Taxing Wages Statistics - SourceOCDE Statistiques des impots sur les salaires     Full-text available via subscription  
Stata Journal     Full-text available via subscription   (Followers: 9)
Statistica Neerlandica     Hybrid Journal   (Followers: 1)
Statistical Applications in Genetics and Molecular Biology     Hybrid Journal   (Followers: 5)
Statistical Communications in Infectious Diseases     Hybrid Journal  
Statistical Inference for Stochastic Processes     Hybrid Journal   (Followers: 3)
Statistical Methodology     Hybrid Journal   (Followers: 7)
Statistical Methods and Applications     Hybrid Journal   (Followers: 6)
Statistical Methods in Medical Research     Hybrid Journal   (Followers: 27)
Statistical Modelling     Hybrid Journal   (Followers: 19)
Statistical Papers     Hybrid Journal   (Followers: 4)
Statistical Science     Full-text available via subscription   (Followers: 13)
Statistics & Probability Letters     Hybrid Journal   (Followers: 13)
Statistics & Risk Modeling     Hybrid Journal   (Followers: 2)
Statistics and Computing     Hybrid Journal   (Followers: 13)
Statistics and Economics     Open Access   (Followers: 1)
Statistics in Medicine     Hybrid Journal   (Followers: 191)
Statistics, Politics and Policy     Hybrid Journal   (Followers: 6)
Statistics: A Journal of Theoretical and Applied Statistics     Hybrid Journal   (Followers: 14)
Stochastic Models     Hybrid Journal   (Followers: 3)
Stochastics An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Reports     Hybrid Journal   (Followers: 2)
Structural and Multidisciplinary Optimization     Hybrid Journal   (Followers: 12)
Teaching Statistics     Hybrid Journal   (Followers: 7)
Technology Innovations in Statistics Education (TISE)     Open Access   (Followers: 2)
TEST     Hybrid Journal   (Followers: 3)
The American Statistician     Full-text available via subscription   (Followers: 24)
The Annals of Applied Probability     Full-text available via subscription   (Followers: 8)
The Annals of Probability     Full-text available via subscription   (Followers: 10)
The Annals of Statistics     Full-text available via subscription   (Followers: 34)
The Canadian Journal of Statistics / La Revue Canadienne de Statistique     Hybrid Journal   (Followers: 11)
Wiley Interdisciplinary Reviews - Computational Statistics     Hybrid Journal   (Followers: 1)

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Similar Journals
Journal Cover
Journal of Global Optimization
Journal Prestige (SJR): 1.311
Citation Impact (citeScore): 2
Number of Followers: 7  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2916 - ISSN (Online) 0925-5001
Published by Springer-Verlag Homepage  [2626 journals]
  • A general branch-and-bound framework for continuous global multiobjective
           optimization
    • Abstract: Abstract Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and by the corresponding termination criteria and node selection steps. In particular, our branch-and-bound concept employs a new enclosure of the set of nondominated points by a union of boxes. On this occasion we also suggest a new discarding test based on a linearization technique. We provide a convergence proof for our general branch-and-bound framework and illustrate the results with numerical examples.
      PubDate: 2021-01-19
       
  • A dual approach to multi-dimensional assignment problems
    • Abstract: Abstract In this paper, we extend the purely dual formulation that we recently proposed for the three-dimensional assignment problems to solve the more general multidimensional assignment problem. The convex dual representation is derived and its relationship to the Lagrangian relaxation method that is usually used to solve multidimensional assignment problems is investigated. Also, we discuss the condition under which the duality gap is zero. It is also pointed out that the process of Lagrangian relaxation is essentially equivalent to one of relaxing the binary constraint condition, thus necessitating the auction search operation to recover the binary constraint. Furthermore, a numerical algorithm based on the dual formulation along with a local search strategy is presented. The simulation results show that the proposed algorithm outperforms the traditional Lagrangian relaxation approach in terms of both accuracy and computational efficiency.
      PubDate: 2021-01-18
       
  • Resolving sets and integer programs for recommender systems
    • Abstract: Abstract Recommender systems make use of different sources of information for providing users with recommendations of items. Such systems are often based on either collaborative filtering methods which make automatic predictions about the interests of a user, using preferences of similar users, or content based filtering that matches the user’s personal preferences with item characteristics. We adopt the content-based approach and propose to use the concept of resolving set that allows to determine the preferences of the users with a very limited number of ratings. We also show how to make recommendations when user ratings are imprecise or inconsistent, and we indicate how to take into account situations where users possibly don’t care about the attribute values of some items. All recommendations are obtained in a few seconds by solving integer programs.
      PubDate: 2021-01-09
       
  • Cheaper relaxation and better approximation for multi-ball constrained
           quadratic optimization and extension
    • Abstract: Abstract We propose a convex quadratic programming (CQP) relaxation for multi-ball constrained quadratic optimization (MB). (CQP) is shown to be equivalent to semidefinite programming relaxation in the hard case. Based on (CQP), we propose an algorithm for solving (MB), which returns a solution of (MB) with an approximation bound independent of the number of constraints. The approximation algorithm is further extended to solve nonconvex quadratic optimization with more general constraints. As an application, we propose a standard quadratic programming relaxation for finding Chebyshev center of a general convex set with a guaranteed approximation bound.
      PubDate: 2021-01-09
       
  • Convexification of bilinear forms through non-symmetric lifting
    • Abstract: Abstract We efficiently treat bilinear forms in the context of global optimization, by applying McCormick convexification and by extending an approach of Saxena et al. (Math Prog Ser B 124(1–2):383–411, 2010) for symmetric quadratic forms to bilinear forms. A key application of our work is in treating “structural convexity” in a symmetric quadratic form.
      PubDate: 2021-01-07
       
  • On global subdifferentials with applications in nonsmooth optimization
    • Abstract: The notions of global subdifferentials associated with the global directional derivatives are introduced in the following paper. Most common used properties, a set of calculus rules along with a mean value theorem are presented as well. In addition, a diversity of comparisons with well-known subdifferentials such as Fréchet, Dini, Clarke, Michel–Penot, and Mordukhovich subdifferential and convexificator notion are provided. Furthermore, the lower global subdifferential is in fact proved to be an abstract subdifferential. Therefore, the lower global subdifferential satisfies standard properties for subdifferential operators. Finally, two applications in nonconvex nonsmooth optimization are given: necessary and sufficient optimality conditions for a point to be local minima with and without constraints, and a revisited characterization for nonsmooth quasiconvex functions.
      PubDate: 2021-01-06
       
  • The EMS vehicle patient transportation problem during a demand surge
    • Abstract: Abstract We consider a real-time emergency medical service (EMS) vehicle patient transportation problem in which vehicles are assigned to patients so they can be transported to hospitals during an emergency. The objective is to minimize the total travel time of all vehicles while satisfying two types of time window constraints. The first requires each EMS vehicle to arrive at a patient’s location within a specified time window. The second requires the vehicle to arrive at the designated hospital within another time window. We allow an EMS vehicle to serve up to two patients instead of just one. The problem is shown to be NP-complete. We, therefore, develop a simulated annealing (SA) heuristic for efficient solution in real-time. A column generation algorithm is developed for determining a tight lower bound. Numerical results show that the proposed SA heuristic provides high-quality solutions in much less CPU time, when compared to the general-purpose solver. Therefore, it is suitable for implementation in a real-time decision support system, which is available via a web portal (www.rtdss.org).
      PubDate: 2021-01-04
       
  • Solving unconstrained 0-1 polynomial programs through quadratic convex
           reformulation
    • Abstract: Abstract We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by adding new binary variables and reformulating (UBP) into a non-convex quadratic program with linear constraints (MIQP). We then consider the solution of (MIQP) with a specially-tailored quadratic convex reformulation method. In particular, this method relies, in a pre-processing step, on the resolution of a semi-definite programming problem where the link between initial and additional variables is used. We present computational results where we compare PQCR with the solvers Baron and Scip. We evaluate PQCR on instances of the image restoration problem and the low auto-correlation binary sequence problem from MINLPLib. For this last problem, 33 instances were unsolved in MINLPLib. We solve to optimality 10 of them, and for the 23 others we significantly improve the dual bounds. We also improve the best known solutions of many instances.
      PubDate: 2021-01-04
       
  • A robust method based on LOVO functions for solving least squares problems
    • Abstract: Abstract The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting models to them. This work presents a low order-value optimization (LOVO) version of the Levenberg–Marquardt algorithm, which is well suited to deal with outliers in fitting problems. A general algorithm is presented and convergence to stationary points is demonstrated. Numerical results show that the algorithm is successfully able to detect and ignore outliers without too many specific parameters. Parallel and distributed executions of the algorithm are also possible, allowing the use of larger datasets. Comparison against publicly available robust algorithms shows that the present approach is able to find better adjustments in well known statistical models.
      PubDate: 2021-01-04
       
  • Learning chordal extensions
    • Abstract: Abstract A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension is not a mathematically understood task. For this reason, we follow the current research trend of looking at Combinatorial Optimization tasks by using a Machine Learning lens, and we devise a framework for learning elimination rules yielding high-quality chordal extensions. As a first building block of the learning framework, we propose an imitation learning scheme that mimics the elimination ordering provided by an expert rule. Results show that our imitation learning approach is effective in learning two classical elimination rules: the minimum degree and minimum fill-in heuristics, using simple Graph Neural Network models with only a handful of parameters. Moreover, the learned policies display remarkable generalization performance, across both graphs of larger size, and graphs from a different distribution.
      PubDate: 2021-01-04
       
  • Inexact stochastic subgradient projection method for stochastic
           equilibrium problems with nonmonotone bifunctions: application to expected
           risk minimization in machine learning
    • Abstract: Abstract This paper discusses a stochastic equilibrium problem for which the function is in the form of the expectation of nonmonotone bifunctions and the constraint set is closed and convex. This problem includes various applications such as stochastic variational inequalities, stochastic Nash equilibrium problems, and nonconvex stochastic optimization problems. For solving this stochastic equilibrium problem, we propose an inexact stochastic subgradient projection method. The proposed method sets a random realization of the bifunction and then updates its approximation by using both its stochastic subgradient and the projection onto the constraint set. The main contribution of this paper is to present a convergence analysis showing that, under certain assumptions, any accumulation point of the sequence generated by the proposed method using a constant step size almost surely belongs to the solution set of the stochastic equilibrium problem. A convergence rate analysis of the method is also provided to illustrate the method’s efficiency. Another contribution of this paper is to show that a machine learning algorithm based on the proposed method achieves the expected risk minimization for a class of least absolute selection and shrinkage operator (lasso) problems in statistical learning with sparsity. Numerical comparisons of the proposed machine learning algorithm with existing machine learning algorithms for the expected risk minimization using LIBSVM datasets demonstrate the effectiveness and superior classification accuracy of the proposed algorithm.
      PubDate: 2021-01-04
       
  • Multi-objective convex polynomial optimization and semidefinite
           programming relaxations
    • Abstract: Abstract This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization problem  \(({\mathrm{P}}_{z})\) and does not destroy the properties of convexity, is considered. First, we show an existence result for efficient solutions to problem (MP) under some mild assumption. Then, for problem  \((P_{z})\) , we establish two kinds of representations of non-negativity of convex polynomials over convex semi-algebraic sets, and propose two kinds of finite convergence results of the Lasserre-type hierarchy of semidefinite programming relaxations for problem  \(({\mathrm{P}}_{z})\) under suitable assumptions. Finally, we show that finding efficient solutions to problem (MP) can be achieved successfully by solving hierarchies of semidefinite programming relaxations and checking a flat truncation condition.
      PubDate: 2021-01-04
       
  • On tackling reverse convex constraints for non-overlapping of unequal
           circles
    • Abstract: Abstract We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield unsatisfactory loose relaxations. Consequently, solving such non-convex models to guaranteed optimality remains extremely challenging even for the state-of-the-art codes. In this paper, we apply a purpose-built branching scheme on non-overlapping constraints and utilize strengthened intersection cuts and various feasibility-based tightening techniques to further tighten the model relaxation. We embed these techniques into a branch-and-bound code and test them on two variants of circle packing problems. Our computational studies on a suite of 75 benchmark instances yielded, for the first time in the open literature, a total of 54 provably optimal solutions, and it was demonstrated to be competitive over the use of the state-of-the-art general-purpose global optimization solvers.
      PubDate: 2021-01-04
       
  • An exact separation algorithm for unsplittable flow capacitated network
           design arc-set polyhedron
    • Abstract: Abstract In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by solving the separation problem over it. To relieve the computational burden, we show that, in some special cases, a closed form of the separation problem can be derived. For the general case, a brute-force algorithm, called exact separation algorithm, is employed in solving the separation problem of the considered polyhedron such that the constructed inequality guarantees to be facet-defining. Furthermore, a new technique is presented to accelerate the exact separation algorithm, which significantly decreases the number of iterations in the algorithm. Finally, a comprehensive computational study on the unsplittable capacitated network design problem is presented to demonstrate the effectiveness of the proposed algorithm.
      PubDate: 2021-01-04
       
  • Stochastic optimization with adaptive restart: a framework for integrated
           local and global learning
    • Abstract: Abstract A common approach to global optimization is to combine local optimization methods with random restarts. Restarts have been used as a performance boosting approach. They can be a means to avoid “slow progress” by exploiting a potentially good solution, and restarts can enable the potential discovery of multiple local solutions, thus improving the overall quality of the returned solution. A multi-start method is a way to integrate local and global approaches; where the global search itself can be used to restart a local search. Bayesian optimization methods aim to find global optima of functions that can only be point-wise evaluated by means of a possibly expensive oracle. We propose the stochastic optimization with adaptive restart (SOAR) framework, that uses the predictive capability of Gaussian process models as a means to adaptively restart local search and intelligently select restart locations with current information. This approach attempts to balance exploitation with exploration of the solution space. We study the asymptotic convergence of SOAR to a global optimum, and empirically evaluate SOAR performance through a specific implementation that uses the Trust Region method as the local search component. Numerical experiments show that the proposed algorithm outperforms existing methodologies over a suite of test problems of varying problem dimension with a finite budget of function evaluations.
      PubDate: 2021-01-01
       
  • Oscars-ii : an algorithm for bound constrained global optimization
    • Abstract: Abstract An adaptation of the oscars algorithm for bound constrained global optimization is presented, and numerically tested. The algorithm is a stochastic direct search method, and has low overheads which are constant per sample point. Some sample points are drawn randomly in the feasible region from time to time, ensuring global convergence almost surely under mild conditions. Additional sample points are preferentially placed near previous good sample points to improve the rate of convergence. Connections with partitioning strategies are explored for oscars and the new method, showing these methods have a reduced risk of sample point redundancy. Numerical testing shows that the method is viable in practice, and is substantially faster than oscars in 4 or more dimensions. Comparison with other methods shows good performance in moderately high dimensions. A power law test for identifying and avoiding proper local minima is presented and shown to give modest improvement.
      PubDate: 2021-01-01
       
  • The extreme rays of the $$6\times 6$$ 6 × 6 copositive cone
    • Abstract: Abstract We provide a complete classification of the extreme rays of the \(6 \times 6\) copositive cone \(\mathcal {COP}^{6}\) . We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix \(A \in \mathcal {COP}^{6}\) . To each such minimal zero support set we construct a stratified semi-algebraic manifold in the space of real symmetric \(6 \times 6\) matrices \({\mathcal {S}}^{6}\) , parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices \(A \in \mathcal {COP}^{6}\) having this minimal zero support set. Each semi-algebraic stratum is characterized by the supports of the minimal zeros u as well as the supports of the corresponding matrix-vector products Au. The analysis uses recently and newly developed methods that are applicable to copositive matrices of arbitrary order.
      PubDate: 2021-01-01
       
  • Second-order KKT optimality conditions for multiobjective discrete optimal
           control problems
    • Abstract: This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense of Pareto to a class of multi-objective discrete optimal control problems with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order optimality conditions for a multi-objective mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a multi-objective discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.
      PubDate: 2021-01-01
       
  • Resolving learning rates adaptively by locating stochastic non-negative
           associated gradient projection points using line searches
    • Abstract: Abstract Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. Attempts to resolve learning rates adaptively, using line searches, have proven computationally demanding. Reducing the computational cost by considering mini-batch sub-sampling (MBSS) introduces challenges due to significant variance in information between batches that may present as discontinuities in the loss function, depending on the MBSS approach. This study proposes a robust approach to adaptively resolve learning rates in dynamic MBSS loss functions. This is achieved by finding sign changes from negative to positive along directional derivatives, which ultimately converge to a stochastic non-negative associated gradient projection point. Through a number of investigative studies, we demonstrate that gradient-only line searches (GOLS) resolve learning rates adaptively, improving convergence performance over minimization line searches, ignoring certain local minima and eliminating an otherwise expensive hyperparameter. We also show that poor search directions may benefit computationally from overstepping optima along a descent direction, which can be resolved by considering improved search directions. Having shown that GOLS is a reliable line search allows for comparative investigations between static and dynamic MBSS.
      PubDate: 2021-01-01
       
  • Weak convergence of an extended splitting method for monotone inclusions
    • Abstract: Abstract In this article, we consider the problem of finding zeros of monotone inclusions of three operators in real Hilbert spaces, where the first operator’s inverse is strongly monotone and the third is linearly composed, and we suggest an extended splitting method. This method allows relative errors and is capable of decoupling the third operator from linear composition operator well. At each iteration, the first operator can be processed with just a single forward step, and the other two need individual computations of the resolvents. If the first operator vanishes and linear composition operator is the identity one, then it coincides with a known method. Under the weakest possible conditions, we prove its weak convergence of the generated primal sequence of the iterates by developing a more self-contained and less convoluted techniques. Our suggested method contains one parameter. When it is taken to be either zero or two, our suggested method has interesting relations to existing methods. Furthermore, we did numerical experiments to confirm its efficiency and robustness, compared with other state-of-the-art methods.
      PubDate: 2021-01-01
       
 
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