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Numerical Functional Analysis and Optimization最新文献

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Lagrange Duality and Saddle Point Optimality Conditions for Multiobjective Semi-Infinite Programming with Vanishing Constraints 带消失约束条件的多目标半无限编程的拉格朗日对偶性和鞍点最优条件
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-02-02 DOI: 10.1080/01630563.2024.2305347
Le Thanh Tung, Dang Hoang Tam, Tran Thien Khai
{"title":"Lagrange Duality and Saddle Point Optimality Conditions for Multiobjective Semi-Infinite Programming with Vanishing Constraints","authors":"Le Thanh Tung, Dang Hoang Tam, Tran Thien Khai","doi":"10.1080/01630563.2024.2305347","DOIUrl":"https://doi.org/10.1080/01630563.2024.2305347","url":null,"abstract":"The objective of this paper is to investigate multiobjective semi-infinite programming problems with vanishing constraints (in brief, MSIPVC). We firstly propose both the vector Lagrange dual probl...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139665699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Radius of S-Quasimonotone Maps S 夸西蒙诺顿映射的稳定半径
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-01-26 DOI: 10.1080/01630563.2024.2305345
V. T. T. Binh, P. T. An
{"title":"Stability Radius of S-Quasimonotone Maps","authors":"V. T. T. Binh, P. T. An","doi":"10.1080/01630563.2024.2305345","DOIUrl":"https://doi.org/10.1080/01630563.2024.2305345","url":null,"abstract":"","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139595012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bivariate Bernstein Chlodovsky Operators Preserving Exponential Functions and Their Convergence Properties 保留指数函数的双变量伯恩斯坦克洛多夫斯基算子及其收敛特性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-12-29 DOI: 10.1080/01630563.2023.2297439
Tuncer Acar, Murat Bodur, Esma Isikli
{"title":"Bivariate Bernstein Chlodovsky Operators Preserving Exponential Functions and Their Convergence Properties","authors":"Tuncer Acar, Murat Bodur, Esma Isikli","doi":"10.1080/01630563.2023.2297439","DOIUrl":"https://doi.org/10.1080/01630563.2023.2297439","url":null,"abstract":"This paper is devoted to an extension of the bivariate generalized Bernstein-Chlodovsky operators preserving the exponential function exp (2,2) where exp (α,β)=e−αx−βy,α,β∈R0+ and x,y≥0. For thes...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local Error Bounds for Affine Variational Inequalities on Hilbert Spaces 希尔伯特空间上仿变分不等式的局部误差界值
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-12-27 DOI: 10.1080/01630563.2023.2297426
Lim Yongdo, Ngoc Tuan Hoang, Dong Yen Nguyen
{"title":"Local Error Bounds for Affine Variational Inequalities on Hilbert Spaces","authors":"Lim Yongdo, Ngoc Tuan Hoang, Dong Yen Nguyen","doi":"10.1080/01630563.2023.2297426","DOIUrl":"https://doi.org/10.1080/01630563.2023.2297426","url":null,"abstract":"This paper gives some results related to the research problem about infinite-dimensional affine variational inequalities raised by N.D. Yen and X. Yang [Affine variational inequalities on normed sp...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Approach for Solving Split Common Fixed Point Problems with Multiple Output Sets That Uses Dynamic Step Sizes 一种使用动态步长求解多输出集分裂公共不动点问题的方法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-11-10 DOI: 10.1080/01630563.2023.2278836
Huanhuan Cui
{"title":"An Approach for Solving Split Common Fixed Point Problems with Multiple Output Sets That Uses Dynamic Step Sizes","authors":"Huanhuan Cui","doi":"10.1080/01630563.2023.2278836","DOIUrl":"https://doi.org/10.1080/01630563.2023.2278836","url":null,"abstract":"AbstractIn this paper, we investigate the split common fixed point problem with multiple output sets and develop novel approaches for effectively approximating its solution. We establish two convergence theorems under appropriate conditions for strictly pseudo-contractive mappings and demicontractive mappings, respectively, which cover some existing results as a special case. Furthermore, the numerical experiments demonstrate that we have developed a competitive method for solving the split common fixed point problem with multiple output sets.KEYWORDS: Demiclosedness principledemicontractive mapsplit common fixed point problemstrictly pseudo-contractive mapMATHEMATICS SUBJECT CLASSIFICATION: 47J2547H0947H1047J05 AcknowledgmentsWe would like to extend our appreciation to the reviewers for their constructive comments that significantly enhanced the quality of our work.Additional informationFundingThis work is supported by the National Natural Science Foundation of China (No. 12101286, 11971216).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135185944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How Averaged is the Composition of Two Linear Projections? 两个线性投影的合成有多平均?
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-29 DOI: 10.1080/01630563.2023.2270308
Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi
{"title":"How Averaged is the Composition of Two Linear Projections?","authors":"Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi","doi":"10.1080/01630563.2023.2270308","DOIUrl":"https://doi.org/10.1080/01630563.2023.2270308","url":null,"abstract":"AbstractProjection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this note, we introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura–Yamada bound for the modulus of the composition is sharp.KEYWORDS: Averaged mappingFriedrichs anglemodulus of averagednessnonexpansive mappingOgura–Yamada boundprojectionMATHEMATICS SUBJECT CLASSIFICATION: Primary: 47H09Secondary: 65K0590C25 AcknowledgmentsThe authors thank the reviewers and the editors for careful reading and constructive comments. We also thank Dr. Andrzej Cegielski for making us aware of his recent work [Citation3] which contains complementary results.Notes1 Usually, one excludes the cases κ = 0 and κ = 1 in the study of averaged operators, but it is very convenient in this paper to allow for this case.2 We assume for convenience throughout the paper that the operators have full domain which is the case in all algorithmic applications we are aware of. One could obviously generalize this notion to allow for operators whose domains are proper subsets of X.Additional informationFundingThe research of the authors was partially supported by Discovery Grants of the Natural Sciences and Engineering Research Council of Canada.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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-Like Algorithm for Solving Common Fixed Point Problems of a Family of Continuous Pseudocontractive Mappings 一类连续伪压缩映射的公共不动点问题的类惯性算法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-27 DOI: 10.1080/01630563.2023.2267352
H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay
{"title":"An Inertial-Like Algorithm for Solving Common Fixed Point Problems of a Family of Continuous Pseudocontractive Mappings","authors":"H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay","doi":"10.1080/01630563.2023.2267352","DOIUrl":"https://doi.org/10.1080/01630563.2023.2267352","url":null,"abstract":"AbstractIn this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm.Keywords: Common fixed pointcontinuous mappingHilbert spaceinertial methodpseudocontaractive mappingMATHEMATICS SUBJECT CLASSIFICATION: 46N1047B0247H0547H0947H1047J2547J26 Additional informationFundingYA Belay is grateful for the financial support from Simons Foundation based at Botswana International University of Science and Technology (BIUST).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding the Best Proximity Point of Generalized Multivalued Contractions with Applications 广义多值压缩的最佳接近点的寻找及其应用
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-18 DOI: 10.1080/01630563.2023.2267294
Deepesh Kumar Patel, Bhupeshwar Patel
{"title":"Finding the Best Proximity Point of Generalized Multivalued Contractions with Applications","authors":"Deepesh Kumar Patel, Bhupeshwar Patel","doi":"10.1080/01630563.2023.2267294","DOIUrl":"https://doi.org/10.1080/01630563.2023.2267294","url":null,"abstract":"AbstractThis paper introduces new kind of algorithms for multivalued non-self mapping to obtain the best proximity point without assuming the continuity of involved mapping. Some non-trivial examples are presented to illustrate the facts. Consequently, an application to finding an optimal approximate solution for the homotopy theory is also discussed.Keywords: Best proximity pointFeng-Liu type F-contractionmultivalued almost F-contractionweak P-property and homotopyMATHEMATICS SUBJECT CLASSIFICATION: 47H1054H2554E50 AcknowledgmentsThe authors would like to thank the editor and reviewers for their valuable comments.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations 结合hessian驱动阻尼和Tikhonov正则化的惯性动力学下轨迹的强收敛
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-17 DOI: 10.1080/01630563.2023.2262828
Akram Chahid Bagy, Zaki Chbani, Hassan Riahi
{"title":"Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations","authors":"Akram Chahid Bagy, Zaki Chbani, Hassan Riahi","doi":"10.1080/01630563.2023.2262828","DOIUrl":"https://doi.org/10.1080/01630563.2023.2262828","url":null,"abstract":"AbstractLet H be a real Hilbert space, and f:H→R be a convex twice differentiable function whose solution set argminf is nonempty. We investigate the long time behavior of the trajectories of the vanishing damped dynamical system with Tikhonov regularizing term and Hessian-driven damping x¨(t)+α x˙(t)+δ∇2f(x(t))x˙(t)+β(t)∇f(x(t))+cx(t)=0 where α,c,δ are three positive constants, and the time scale parameter β is a positive nondecreasing function such that limt→+∞β(t)=+∞. Under some assumptions on the parameter β, we will show rapid convergence of values, strong convergence toward the minimum norm element of argminf, and rapid convergence of the gradients toward zero. Note that the Hessian-driven damping significantly reduces the oscillatory aspects, and the time scale parameter β improves the rate of convergences mentioned above. As particular cases of β, we set β(t)=tp ln q(t), for (p,q)∈(R+)2∖{(0,0)}, and β(t)=eγtp, for p∈]0,1[ and γ>0. The manuscript concludes with two numerical examples and comments on their performance.KEYWORDS: Damped dynamical systemfast convergenceHessian-driven dampingHilbert spacestrong convergenceTikhonov regularizationMATHEMATICS SUBJECT CLASSIFICATION: 37N4046N1049M3065K0565K1090B5090C25","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Proximal Algorithms with Inertial Effects Beyond Monotonicity 超越单调性的惯性效应的近端算法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-13 DOI: 10.1080/01630563.2023.2266762
Alfredo N. Iusem, R. T. Marcavillaca
{"title":"On Proximal Algorithms with Inertial Effects Beyond Monotonicity","authors":"Alfredo N. Iusem, R. T. Marcavillaca","doi":"10.1080/01630563.2023.2266762","DOIUrl":"https://doi.org/10.1080/01630563.2023.2266762","url":null,"abstract":"AbstractInertial procedures attached to classical methods for solving monotone inclusion and optimization problems, which arise from an implicit discretization of second-order differential equations, have shown a remarkable acceleration effect with respect to these classical algorithms. Among these classical methods, one can mention steepest descent, alternate directions, and the proximal point methods. For the problem of finding zeroes of set-valued operators, the convergence analysis of all existing inertial-proximal methods requires the monotonicity of the operator. We present here a new inertial-proximal point algorithm for finding zeroes of set-valued operators, whose convergence is established for a relevant class of nonmonotone operators, namely the hypomonotone ones.KEYWORDS: Generalized monotone operatorshypomonotone operatorsinertial methodsproximal point methodMATHEMATICS SUBJECT CLASSIFICATION: 90C2590C3047H05","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135859122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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