Optimization Methods and Software最新文献_第5页

Feasible Newton methods for symmetric tensor Z-eigenvalue problems 对称张量z特征值问题的可行牛顿方法

Optimization Methods and Software Pub Date : 2022-11-14 DOI: 10.1080/10556788.2022.2142586

Jiefeng Xu, Donghui Li, Xueli Bai

引用次数: 1

Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium 能源市场的非凸均衡模型:利用价格信息来确定均衡的存在

Optimization Methods and Software Pub Date : 2022-11-11 DOI: 10.1080/10556788.2022.2117358

Julia Grübel, Olivier Huber, Lukas Hümbs, Max Klimm, Martin Schmidt, Alexandra Schwartz

{"title":"Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium","authors":"Julia Grübel, Olivier Huber, Lukas Hümbs, Max Klimm, Martin Schmidt, Alexandra Schwartz","doi":"10.1080/10556788.2022.2117358","DOIUrl":"https://doi.org/10.1080/10556788.2022.2117358","url":null,"abstract":"Motivated by examples from the energy sector, we consider market equilibrium problems (MEPs) involving players with nonconvex strategy spaces or objective functions, where the latter are assumed to be linear in market prices. We propose an algorithm that determines if an equilibrium of such an MEP exists and that computes an equilibrium in case of existence. Three key prerequisites have to be met. First, appropriate bounds on market prices have to be derived from necessary optimality conditions of some players. Second, a technical assumption is required for those prices that are not uniquely determined by the derived bounds. Third, nonconvex optimization problems have to be solved to global optimality. We test the algorithm on well-known instances from the power and gas literature that meet these three prerequisites. There, nonconvexities arise from considering the transmission system operator as an additional player besides producers and consumers who, e.g. switches lines or faces nonlinear physical laws. Our numerical results indicate that equilibria often exist, especially for the case of continuous nonconvexities in the context of gas market problems.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133639940","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: 1

An approximate Newton-type proximal method using symmetric rank-one updating formula for minimizing the nonsmooth composite functions 利用对称秩一更新公式求非光滑复合函数极小化的近似牛顿型近端方法

Optimization Methods and Software Pub Date : 2022-11-11 DOI: 10.1080/10556788.2022.2142587

Z. Aminifard, S. Babaie-Kafaki

引用次数: 1

Non-convex regularization and accelerated gradient algorithm for sparse portfolio selection 稀疏组合选择的非凸正则化和加速梯度算法

Optimization Methods and Software Pub Date : 2022-11-10 DOI: 10.1080/10556788.2022.2142580

Qian Li, Wei Zhang, Guoqiang Wang, Yanqin Bai

{"title":"Non-convex regularization and accelerated gradient algorithm for sparse portfolio selection","authors":"Qian Li, Wei Zhang, Guoqiang Wang, Yanqin Bai","doi":"10.1080/10556788.2022.2142580","DOIUrl":"https://doi.org/10.1080/10556788.2022.2142580","url":null,"abstract":"In portfolio optimization, non-convex regularization has recently been recognized as an important approach to promote sparsity, while countervailing the shortcomings of convex penalty. In this paper, we customize the non-convex piecewise quadratic approximation (PQA) function considering the background of portfolio management and present the PQA regularized mean–variance model (PMV). By exposing the feature of PMV, we prove that a KKT point of PMV is a local minimizer if the regularization parameter satisfies a mild condition. Besides, the theoretical sparsity of PMV is analysed, which is associated with the regularization parameter and the weight parameter. To solve this model, we introduce the accelerated proximal gradient (APG) algorithm, whose improved linear convergence rate compared with proximal gradient (PG) algorithm is developed. Moreover, the optimal accelerated parameter of APG algorithm for PMV is attained. These theoretical results are further illustrated with numerical experiments. Finally, empirical analysis demonstrates that the proposed model has a better out-of-sample performance and a lower turnover than many other existing models on the tested datasets.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129029857","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: 1

Sparse convex optimization toolkit: a mixed-integer framework 稀疏凸优化工具箱:一个混合整数框架

Optimization Methods and Software Pub Date : 2022-10-30 DOI: 10.1080/10556788.2023.2222429

A. Olama, E. Camponogara, Jan Kronqvist

{"title":"Sparse convex optimization toolkit: a mixed-integer framework","authors":"A. Olama, E. Camponogara, Jan Kronqvist","doi":"10.1080/10556788.2023.2222429","DOIUrl":"https://doi.org/10.1080/10556788.2023.2222429","url":null,"abstract":"This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization Toolkit (SCOT) adopts a mixed-integer approach to find exact solutions to SCO problems. In particular, SCOT brings together various techniques to transform the original SCO problem into an equivalent convex Mixed-Integer Nonlinear Programming (MINLP) problem that can benefit from high-performance and parallel computing platforms. To solve the equivalent mixed-integer problem, we present the Distributed Hybrid Outer Approximation (DiHOA) algorithm that builds upon the LP/NLP based branch-and-bound and is tailored for this specific problem structure. The DiHOA algorithm combines the so-called single- and multi-tree outer approximation, naturally integrates a decentralized algorithm for distributed convex nonlinear subproblems, and utilizes enhancement techniques such as quadratic cuts. Finally, we present detailed computational experiments that show the benefit of our solver through numerical benchmarks on 140 SCO problems with distributed datasets. To show the overall efficiency of SCOT we also provide performance profiles comparing SCOT to other state-of-the-art MINLP solvers.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115584004","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

Linear programming with nonparametric penalty programs and iterated thresholding 非参数惩罚规划与迭代阈值的线性规划

Optimization Methods and Software Pub Date : 2022-10-13 DOI: 10.1080/10556788.2022.2117356

Jeffery Kline, Glenn M. Fung

引用次数: 0

Implementation of a projection and rescaling algorithm for second-order conic feasibility problems 二阶经济可行性问题的投影和缩放算法的实现

Optimization Methods and Software Pub Date : 2022-10-06 DOI: 10.1080/10556788.2022.2119234

Javier F. Pena, Negar Soheili

引用次数: 0

On minty variational principle for quasidifferentiable vector optimization problems 拟可微向量优化问题的极小变分原理

Optimization Methods and Software Pub Date : 2022-09-30 DOI: 10.1080/10556788.2022.2119235

H. Singh, Vivek Laha

引用次数: 1

HyKKT: a hybrid direct-iterative method for solving KKT linear systems HyKKT:求解KKT线性系统的混合直接迭代法

Optimization Methods and Software Pub Date : 2022-09-27 DOI: 10.1080/10556788.2022.2124990

Shaked Regev, Nai-yuan Chiang, Eric F Darve, C. Petra, M. Saunders, K. Swirydowicz, Slaven Pelevs

引用次数: 5

Stochastic distributed learning with gradient quantization and double-variance reduction 基于梯度量化和双方差约简的随机分布式学习

Optimization Methods and Software Pub Date : 2022-09-27 DOI: 10.1080/10556788.2022.2117355

Samuel Horváth, D. Kovalev, Konstantin Mishchenko, Peter Richtárik, S. Stich

{"title":"Stochastic distributed learning with gradient quantization and double-variance reduction","authors":"Samuel Horváth, D. Kovalev, Konstantin Mishchenko, Peter Richtárik, S. Stich","doi":"10.1080/10556788.2022.2117355","DOIUrl":"https://doi.org/10.1080/10556788.2022.2117355","url":null,"abstract":"ABSTRACT We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in order to reduce the overall communication cost. However, existing methods suffer from a significant slowdown due to additional variance coming from the compression operator and as a result, only converge sublinearly. What is needed is a variance reduction technique for taming the variance introduced by compression. We propose the first methods that achieve linear convergence for arbitrary compression operators. For strongly convex functions with condition number κ, distributed among n machines with a finite-sum structure, each worker having less than m components, we also (i) give analysis for the weakly convex and the non-convex cases and (ii) verify in experiments that our novel variance reduced schemes are more efficient than the baselines. Moreover, we show theoretically that as the number of devices increases, higher compression levels are possible without this affecting the overall number of communications in comparison with methods that do not perform any compression. This leads to a significant reduction in communication cost. Our general analysis allows to pick the most suitable compression for each problem, finding the right balance between additional variance and communication savings. Finally, we also (iii) give analysis for arbitrary quantized updates.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116264618","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: 12