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Applied Set-Valued Analysis and Optimization最新文献

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A new linear convergence method for a Lipschitz pseudomonotone variational inequality Lipschitz伪单调变分不等式的一种新的线性收敛方法
Applied Set-Valued Analysis and Optimization Pub Date : 2021-08-01 DOI: 10.23952/asvao.3.2021.2.06
R. Nwokoye, C. C. Okeke, Y. Shehu
{"title":"A new linear convergence method for a Lipschitz pseudomonotone variational inequality","authors":"R. Nwokoye, C. C. Okeke, Y. Shehu","doi":"10.23952/asvao.3.2021.2.06","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.2.06","url":null,"abstract":"","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"417 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115984207","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
Universal bounds for fixed point iterations via optimal transport metrics 通过最优传输度量的不动点迭代的通用界
Applied Set-Valued Analysis and Optimization Pub Date : 2021-07-31 DOI: 10.23952/asvao.4.2022.3.04
Mario Bravo, T. Champion, R. Cominetti
{"title":"Universal bounds for fixed point iterations via optimal transport metrics","authors":"Mario Bravo, T. Champion, R. Cominetti","doi":"10.23952/asvao.4.2022.3.04","DOIUrl":"https://doi.org/10.23952/asvao.4.2022.3.04","url":null,"abstract":". We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel’skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130403226","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
On Clarke’s subdifferential of marginal functions 论克拉克边际函数的次微分
Applied Set-Valued Analysis and Optimization Pub Date : 2021-07-27 DOI: 10.23952/asvao.3.2021.3.03
G. Bouza, Ernest Quintana, C. Tammer
{"title":"On Clarke’s subdifferential of marginal functions","authors":"G. Bouza, Ernest Quintana, C. Tammer","doi":"10.23952/asvao.3.2021.3.03","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.3.03","url":null,"abstract":"In this short note, we derive an upper estimate of Clarke’s subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127833596","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
Convergence theorems of common solutions of variational inequality and f-fixed point problems in Banach spaces Banach空间中变分不等式公解与f不动点问题的收敛定理
Applied Set-Valued Analysis and Optimization Pub Date : 2021-04-01 DOI: 10.23952/asvao.3.2021.1.06
G. Wega, H. Zegeye
{"title":"Convergence theorems of common solutions of variational inequality and f-fixed point problems in Banach spaces","authors":"G. Wega, H. Zegeye","doi":"10.23952/asvao.3.2021.1.06","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.1.06","url":null,"abstract":"","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"413 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124413836","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
On the approximation error for approximating convex bodies using multiobjective optimization 用多目标优化方法逼近凸体的逼近误差
Applied Set-Valued Analysis and Optimization Pub Date : 2021-03-11 DOI: 10.23952/asvao.3.2021.3.08
Andreas Lohne, Fangyuan Zhao, L. Shao
{"title":"On the approximation error for approximating convex bodies using multiobjective optimization","authors":"Andreas Lohne, Fangyuan Zhao, L. Shao","doi":"10.23952/asvao.3.2021.3.08","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.3.08","url":null,"abstract":"A polyhedral approximation of a convex body can be calculated by solving approximately an associated multiobjective convex program (MOCP). An MOCP can be solved approximately by Benson type algorithms, which compute outer and inner polyhedral approximations of the problem’s upper image. Polyhedral approximations of a convex body can be obtained from polyhedral approximations of the upper image of the associated MOCP. We provide error bounds in terms of the Hausdorff distance for the polyhedral approximation of a convex body in dependence of the stopping criteria of the primal and dual Benson algorithm which is applied to the associated MOCP.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"16 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114132119","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 general split fixed point problem governed by demicontractive mappings in Banach spaces Banach空间中由半收缩映射支配的一般分裂不动点问题
Applied Set-Valued Analysis and Optimization Pub Date : 2020-07-01 DOI: 10.23952/asvao.2.2020.2.07
H. Zegeye, O. A. Boikanyo
{"title":"A general split fixed point problem governed by demicontractive mappings in Banach spaces","authors":"H. Zegeye, O. A. Boikanyo","doi":"10.23952/asvao.2.2020.2.07","DOIUrl":"https://doi.org/10.23952/asvao.2.2020.2.07","url":null,"abstract":". In this paper, we introduce an iterative process, which converges strongly to the solution of a general split fixed point problem governed by demicontractive mappings and prove strong convergence theorems in Banach spaces.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129925493","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
Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings 准无穷映射定点约束非光滑凸优化的并行计算近似法
Applied Set-Valued Analysis and Optimization Pub Date : 2020-04-01 DOI: 10.23952/ASVAO.2.2020.1.01
K. Shimizu, K. Hishinuma, H. Iiduka
{"title":"Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings","authors":"K. Shimizu, K. Hishinuma, H. Iiduka","doi":"10.23952/ASVAO.2.2020.1.01","DOIUrl":"https://doi.org/10.23952/ASVAO.2.2020.1.01","url":null,"abstract":". We present a parallel computing proximal method for solving the problem of minimizing the sum of convex functions over the intersection of fixed point sets of quasi-nonexpansive mappings in a real Hilbert space. We also provide a convergence analysis of the method for constant and diminishing step sizes under certain assumptions as well as a convergence-rate analysis for a diminishing step size. Numerical comparisons show that the performance of the algorithm is comparable with existing subgradient methods.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"118 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141217671","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: 7
Some homogeneous q-difference operators and the associated generalized Hahn polynomials 齐次q-差分算子及其相关的广义Hahn多项式
Applied Set-Valued Analysis and Optimization Pub Date : 2019-08-08 DOI: 10.23952/asvao.1.2019.2.07
H. Srivastava, S. Arjika, A. Kelil
{"title":"Some homogeneous q-difference operators and the associated generalized Hahn polynomials","authors":"H. Srivastava, S. Arjika, A. Kelil","doi":"10.23952/asvao.1.2019.2.07","DOIUrl":"https://doi.org/10.23952/asvao.1.2019.2.07","url":null,"abstract":"In this paper, we first construct the homogeneous $q$-shift operator $widetilde{E}(a,b;D_{q})$ and the homogeneous $q$-difference operator $widetilde{L}(a,b; theta_{xy})$. We then apply these operators in order to represent and investigate generalized Cauchy and a general form of Hahn polynomials. We derive some $q$-identities such as: generating functions, extended generating functions, Mehler's formula and Roger's formula for these $q$-polynomials.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115361670","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: 21
On Theorems of Šiňajová, Rankin and Kuperberg Concerning Spherical Point Configurations 关于球面点构型的Šiňajová、Rankin和Kuperberg定理
Applied Set-Valued Analysis and Optimization Pub Date : 2019-08-02 DOI: 10.23952/asvao.5.2023.2.03
A. Alfakih
{"title":"On Theorems of Šiňajová, Rankin and Kuperberg Concerning Spherical Point Configurations","authors":"A. Alfakih","doi":"10.23952/asvao.5.2023.2.03","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.2.03","url":null,"abstract":"This note presents simple linear algebraic proofs of theorems due to Sinajova, Rankin and Kuperberg concerning spherical point configurations. The common ingredient in these proofs is the use of spherical Euclidean distance matrices and the Perron-Frobenius theorem.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116788504","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 inertial three-operator splitting algorithm with applications to image inpainting 一种惯性三算子分割算法及其在图像绘制中的应用
Applied Set-Valued Analysis and Optimization Pub Date : 2019-04-26 DOI: 10.23952/asvao.1.2019.2.03
Fuying Cui, Yuchao Tang, Yang Yang
{"title":"An inertial three-operator splitting algorithm with applications to image inpainting","authors":"Fuying Cui, Yuchao Tang, Yang Yang","doi":"10.23952/asvao.1.2019.2.03","DOIUrl":"https://doi.org/10.23952/asvao.1.2019.2.03","url":null,"abstract":"The three-operators splitting algorithm is a popular operator splitting method for finding the zeros of the sum of three maximally monotone operators, with one of which is cocoercive operator. In this paper, we propose a class of inertial three-operator splitting algorithm. The convergence of the proposed algorithm is proved by applying the inertial Krasnoselskii-Mann iteration under certain conditions on the iterative parameters in real Hilbert spaces. As applications, we develop an inertial three-operator splitting algorithm to solve the convex minimization problem of the sum of three convex functions, where one of them is differentiable with Lipschitz continuous gradient. Finally, we conduct numerical experiments on a constrained image inpainting problem with nuclear norm regularization. Numerical results demonstrate the advantage of the proposed inertial three-operator splitting algorithms.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128032838","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: 24
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