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Journal of Applied and Numerical Optimization最新文献

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Relaxed Lagrangian duality in convex infinite optimization: Reverse strong duality and optimality 凸无限优化中的松弛拉格朗日对偶:逆强对偶与最优性
Journal of Applied and Numerical Optimization Pub Date : 2021-06-17 DOI: 10.23952/jano.4.2022.1.02
N. Dinh, M. Goberna, M. López, M. Volle
{"title":"Relaxed Lagrangian duality in convex infinite optimization: Reverse strong duality and optimality","authors":"N. Dinh, M. Goberna, M. López, M. Volle","doi":"10.23952/jano.4.2022.1.02","DOIUrl":"https://doi.org/10.23952/jano.4.2022.1.02","url":null,"abstract":"We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse H-strong duality theorems, H-Farkas type lemmas and optimality theorems. Special attention is addressed to infinite and semi-infinite linear optimization problems. To Dinh The Luc on the occasion of his 70th anniversary","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128599517","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
On angles between convex cones 在凸锥之间的角度上
Journal of Applied and Numerical Optimization Pub Date : 2021-05-12 DOI: 10.23952/jano.4.2022.2.02
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
{"title":"On angles between convex cones","authors":"Heinz H. Bauschke, Hui Ouyang, Xianfu Wang","doi":"10.23952/jano.4.2022.2.02","DOIUrl":"https://doi.org/10.23952/jano.4.2022.2.02","url":null,"abstract":"There are two basic angles associated with a pair of linear subspaces: the Diximier angle and the Friedrichs angle. The Dixmier angle of the pair of orthogonal complements is the same as the Dixmier angle of the original pair provided that the original pair gives rise to a direct (not necessarily orthogonal) sum of the underlying Hilbert space. The Friedrichs angles of the original pair and the pair of the orthogonal complements always coincide. These two results are due to Krein, Krasnoselskii, and Milman and to Solmon, respectively. In 1995, Deutsch provided a very nice survey with complete proofs and interesting historical comments. One key result in Deutsch’s survey was an inequality for Dixmier angles provided by Hundal. In this paper, we present extensions of these results to the case when the linear subspaces are only required to be convex cones. It turns out that Hundal’s result has a nice conical extension while the situation is more technical for the results by Krein et al. and by Solmon. Our analysis is based on Deutsch’s survey and our recent work on angles between convex sets. Throughout, we also provide examples illustrating the sharpness of our results.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126098263","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
Problem structures in the theory and practice of superiorization 上级管理理论与实践中的问题结构
Journal of Applied and Numerical Optimization Pub Date : 2019-09-19 DOI: 10.23952/jano.2.2020.1.05
G. Herman
{"title":"Problem structures in the theory and practice of superiorization","authors":"G. Herman","doi":"10.23952/jano.2.2020.1.05","DOIUrl":"https://doi.org/10.23952/jano.2.2020.1.05","url":null,"abstract":"The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently, superiorization is often presented using the terminology of such problems. A more general approach is provided here by discussing ideas related to superiorization in terms of an abstract mathematical concept, referred to as a problem structure.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132748193","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
Differentiating through a cone program 通过一个锥体程序求导
Journal of Applied and Numerical Optimization Pub Date : 2019-04-19 DOI: 10.23952/jano.1.2019.2.02
Akshay Agrawal, Shane T. Barratt, Stephen P. Boyd, Enzo Busseti, W. M. Moursi
{"title":"Differentiating through a cone program","authors":"Akshay Agrawal, Shane T. Barratt, Stephen P. Boyd, Enzo Busseti, W. M. Moursi","doi":"10.23952/jano.1.2019.2.02","DOIUrl":"https://doi.org/10.23952/jano.1.2019.2.02","url":null,"abstract":"We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the linear systems of equations required using an iterative method. This allows us to efficiently compute the derivative operator, and its adjoint, evaluated at a vector. These correspond to computing an approximate new solution, given a perturbation to the cone program coefficients (i.e., perturbation analysis), and to computing the gradient of a function of the solution with respect to the coefficients. Our method scales to large problems, with numbers of coefficients in the millions. We present an open-source Python implementation of our method that solves a cone program and returns the derivative and its adjoint as abstract linear maps; our implementation can be easily integrated into software systems for automatic differentiation.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129134477","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: 97
The Fermat-Torricelli problem and Weiszfeld’s algorithm in the light of convex analysis 基于凸分析的费马-托里拆利问题及Weiszfeld算法
Journal of Applied and Numerical Optimization Pub Date : 2013-02-21 DOI: 10.23952/jano.1.2019.3.02
B. Mordukhovich, N. M. Nam
{"title":"The Fermat-Torricelli problem and Weiszfeld’s algorithm in the light of convex analysis","authors":"B. Mordukhovich, N. M. Nam","doi":"10.23952/jano.1.2019.3.02","DOIUrl":"https://doi.org/10.23952/jano.1.2019.3.02","url":null,"abstract":"In the early 17th century, Pierre de Fermat proposed the following problem: given three points in the plane, find a point such that the sum of its Euclidean distances to the three given points is minimal. This problem was solved by Evangelista Torricelli and was named the {em Fermat-Torricelli problem}. A more general version of the Fermat-Torricelli problem asks for a point that minimizes the sum of the distances to a finite number of given points in $Bbb R^n$. This is one of the main problems in location science. In this paper we revisit the Fermat-Torricelli problem from both theoretical and numerical viewpoints using some ingredients of convex analysis and optimization.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123555673","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: 6
A descent-like method for fixed points and split conclusion problems 不动点和分裂结论问题的类下降方法
Journal of Applied and Numerical Optimization Pub Date : 1900-01-01 DOI: 10.23952/jano.1.2019.1.08
M. Shang
{"title":"A descent-like method for fixed points and split conclusion problems","authors":"M. Shang","doi":"10.23952/jano.1.2019.1.08","DOIUrl":"https://doi.org/10.23952/jano.1.2019.1.08","url":null,"abstract":"In this paper, a descent-like method is introduced for solving a fixed point problem of a strict pseudocontraction and a split variational inclusion problem. A strong convergence theorem of common solutions is established in the framework of Hilbert spaces without any compact assumptions on any mapping.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115282079","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: 6
An inertial splitting algorithm for solving inclusion problems and its applications to compressed sensing 求解包含问题的惯性分裂算法及其在压缩感知中的应用
Journal of Applied and Numerical Optimization Pub Date : 1900-01-01 DOI: 10.23952/jano.2.2020.3.02
{"title":"An inertial splitting algorithm for solving inclusion problems and its applications to compressed sensing","authors":"","doi":"10.23952/jano.2.2020.3.02","DOIUrl":"https://doi.org/10.23952/jano.2.2020.3.02","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115438159","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: 4
The Tseng’s extragradient method for semistrictly quasimonotone variational inequalities 半严格拟单调变分不等式的Tseng微分法
Journal of Applied and Numerical Optimization Pub Date : 1900-01-01 DOI: 10.23952/jano.4.2022.2.06
{"title":"The Tseng’s extragradient method for semistrictly quasimonotone variational inequalities","authors":"","doi":"10.23952/jano.4.2022.2.06","DOIUrl":"https://doi.org/10.23952/jano.4.2022.2.06","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116938313","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: 2
Convergence of inexact iterates of strict contractions in metric spaces with graphs 具有图的度量空间中严格压缩的不精确迭代的收敛性
Journal of Applied and Numerical Optimization Pub Date : 1900-01-01 DOI: 10.23952/jano.4.2022.2.07
{"title":"Convergence of inexact iterates of strict contractions in metric spaces with graphs","authors":"","doi":"10.23952/jano.4.2022.2.07","DOIUrl":"https://doi.org/10.23952/jano.4.2022.2.07","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126832317","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: 5
Semicontinuity of the composition of set-valued map and scalarization function for sets 集值映射与集合标化函数复合的半连续性
Journal of Applied and Numerical Optimization Pub Date : 1900-01-01 DOI: 10.23952/jano.1.2019.3.06
Mengxue Liu, Yuto Ogata, Tamaki Tanaka
{"title":"Semicontinuity of the composition of set-valued map and scalarization function for sets","authors":"Mengxue Liu, Yuto Ogata, Tamaki Tanaka","doi":"10.23952/jano.1.2019.3.06","DOIUrl":"https://doi.org/10.23952/jano.1.2019.3.06","url":null,"abstract":"In this paper, we deal with the inheritation of the semicontinuity of set-valued maps via general scalarization for sets, which is regarded as the framework of generalizations of results by Kuwano, Tanaka, and Yamada in 2010. Since the unified scalarization functions for sets satisfy certain desired semicontinuity, our main theorems can be reduced to the results in earlier study.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114601376","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
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