Optimization Methods and Software最新文献_第10页

Steering exact penalty DCA for nonsmooth DC optimisation problems with equality and inequality constraints 具有等式和不等式约束的非光滑DC优化问题的转向精确惩罚DCA

Optimization Methods and Software Pub Date : 2021-07-03 DOI: 10.1080/10556788.2023.2167992

M. V. Dolgopolik

引用次数: 1

Conic optimization-based algorithms for nonnegative matrix factorization 基于二次优化的非负矩阵分解算法

Optimization Methods and Software Pub Date : 2021-05-28 DOI: 10.1080/10556788.2023.2189714

V. Leplat, Y. Nesterov, Nicolas Gillis, F. Glineur

{"title":"Conic optimization-based algorithms for nonnegative matrix factorization","authors":"V. Leplat, Y. Nesterov, Nicolas Gillis, F. Glineur","doi":"10.1080/10556788.2023.2189714","DOIUrl":"https://doi.org/10.1080/10556788.2023.2189714","url":null,"abstract":"Nonnegative matrix factorization is the following problem: given a nonnegative input matrix V and a factorization rank K, compute two nonnegative matrices, W with K columns and H with K rows, such that WH approximates V as well as possible. In this paper, we propose two new approaches for computing high-quality NMF solutions using conic optimization. These approaches rely on the same two steps. First, we reformulate NMF as minimizing a concave function over a product of convex cones – one approach is based on the exponential cone and the other on the second-order cone. Then, we solve these reformulations iteratively: at each step, we minimize exactly, over the feasible set, a majorization of the objective functions obtained via linearization at the current iterate. Hence these subproblems are convex conic programs and can be solved efficiently using dedicated algorithms. We prove that our approaches reach a stationary point with an accuracy decreasing as , where i denotes the iteration number. To the best of our knowledge, our analysis is the first to provide a convergence rate to stationary points for NMF. Furthermore, in the particular cases of rank-1 factorizations (i.e. K = 1), we show that one of our formulations can be expressed as a convex optimization problem, implying that optimal rank-1 approximations can be computed efficiently. Finally, we show on several numerical examples that our approaches are able to frequently compute exact NMFs (i.e. with V = WH) and compete favourably with the state of the art.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115748319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An incremental descent method for multi-objective optimization 多目标优化的增量下降法

Optimization Methods and Software Pub Date : 2021-05-25 DOI: 10.1080/10556788.2022.2124989

I. F. D. Oliveira, R. Takahashi

引用次数: 1

A majorization penalty method for SVM with sparse constraint 基于稀疏约束的支持向量机的多数化惩罚方法

Optimization Methods and Software Pub Date : 2021-05-15 DOI: 10.1080/10556788.2022.2142584

Si-Tong Lu, Qingna Li

引用次数: 0

Reflected three-operator splitting method for monotone inclusion problem 单调包含问题的反射三算子分裂方法

Optimization Methods and Software Pub Date : 2021-05-12 DOI: 10.1080/10556788.2021.1924715

O. Iyiola, C. Enyi, Y. Shehu

引用次数: 7

Operator splitting for adaptive radiation therapy with nonlinear health dynamics 具有非线性健康动力学的自适应放射治疗算子分裂

Optimization Methods and Software Pub Date : 2021-05-04 DOI: 10.1080/10556788.2022.2078824

A. Fu, L. Xing, Stephen P. Boyd

引用次数: 0

An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems 变分不等式问题的一种自适应步长惯性次梯度外聚算法

Optimization Methods and Software Pub Date : 2021-04-26 DOI: 10.1080/10556788.2021.1910946

Xiaokai Chang, Sanyang Liu, Zhao Deng, Suoping Li

引用次数: 8

A competitive inexact nonmonotone filter SQP method: convergence analysis and numerical results 一种竞争非精确非单调滤波SQP方法:收敛分析及数值结果

Optimization Methods and Software Pub Date : 2021-04-15 DOI: 10.1080/10556788.2021.1913155

Hani Ahmadzadeh, N. Mahdavi-Amiri

{"title":"A competitive inexact nonmonotone filter SQP method: convergence analysis and numerical results","authors":"Hani Ahmadzadeh, N. Mahdavi-Amiri","doi":"10.1080/10556788.2021.1913155","DOIUrl":"https://doi.org/10.1080/10556788.2021.1913155","url":null,"abstract":"We propose an inexact nonmonotone successive quadratic programming (SQP) algorithm for solving nonlinear programming problems with equality constraints and bounded variables. Regarding the value of the current feasibility violation and the minimum value of its linear approximation over a trust region, several scenarios are envisaged. In one scenario, a possible infeasible stationary point is detected. In other scenarios, the search direction is computed using an inexact (truncated) solution of a feasible strictly convex quadratic program (QP). The search direction is shown to be a descent direction for the objective function or the feasibility violation in the feasible or infeasible iterations, respectively. A new penalty parameter updating formula is proposed to turn the search direction into a descent direction for an -penalty function. In certain iterations, an accelerator direction is developed to obtain a superlinear local convergence rate of the algorithm. Using a nonmonotone filter strategy, the global convergence of the algorithm and a superlinear local rate of convergence are guaranteed. The main advantage of the algorithm is that the global convergence of the algorithm is established using inexact solutions of the QPs. Furthermore, the use of inexact solutions instead of exact solutions of the subproblems enhances the robustness and efficiency of the algorithm. The algorithm is implemented using MATLAB and the program is tested on a wide range of test problems from the CUTEst library. Comparison of the obtained numerical results with those obtained by testing some similar SQP algorithms affirms the efficiency and robustness of the proposed algorithm.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115218093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A globally convergent regularized interior point method for constrained optimization 约束优化的全局收敛正则内点法

Optimization Methods and Software Pub Date : 2021-04-05 DOI: 10.1080/10556788.2021.1908283

Songqiang Qiu

引用次数: 1

A primer on the application of neural networks to covering array generation 介绍神经网络在覆盖阵列生成中的应用

Optimization Methods and Software Pub Date : 2021-04-05 DOI: 10.1080/10556788.2021.1907384

Ludwig Kampel, Michael Wagner, I. Kotsireas, D. Simos

{"title":"A primer on the application of neural networks to covering array generation","authors":"Ludwig Kampel, Michael Wagner, I. Kotsireas, D. Simos","doi":"10.1080/10556788.2021.1907384","DOIUrl":"https://doi.org/10.1080/10556788.2021.1907384","url":null,"abstract":"In the past, combinatorial structures have been used only to tune parameters of neural networks. In this work, we employ neural networks in the form of Boltzmann machines and Hopfield networks for the construction of a specific class of combinatorial designs, namely covering arrays (CAs). In past works, these neural networks were successfully used to solve set cover instances. For the construction of CAs, we consider the corresponding set cover instances and use neural networks to solve such instances. We adapt existing algorithms for solving general set cover instances, which are based on Boltzmann machines and Hopfield networks and apply them for CA construction. Furthermore, for the algorithm based on Boltzmann machines, we consider newly designed versions, where we deploy structural changes of the underlying Boltzmann machine, adding a feedback loop. Additionally, one variant of this algorithm employs learning techniques based on neural networks to adjust the various connections encountered in the graph representing the considered set cover instances. Culminating in a comprehensive experimental evaluation, our work presents the first study of applications of neural networks in the field of covering array generation and related discrete structures and may act as a guideline for future investigations.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126629151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0