Pub Date : 2024-02-02DOI: 10.1080/01630563.2024.2305347
Le Thanh Tung, Dang Hoang Tam, Tran Thien Khai
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...
{"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}
Pub Date : 2024-01-26DOI: 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}
Pub Date : 2023-12-29DOI: 10.1080/01630563.2023.2297439
Tuncer Acar, Murat Bodur, Esma Isikli
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...
{"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}
Pub Date : 2023-12-27DOI: 10.1080/01630563.2023.2297426
Lim Yongdo, Ngoc Tuan Hoang, Dong Yen Nguyen
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...
本文给出了与 N.D. Yen 和 X. Yang [Affine variational inequalities on normed sp...] 提出的无穷维仿射变分不等式研究问题相关的一些结果。
{"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}
Pub Date : 2023-11-10DOI: 10.1080/01630563.2023.2278836
Huanhuan Cui
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).
{"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}
Pub Date : 2023-10-29DOI: 10.1080/01630563.2023.2270308
Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi
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.
{"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}
Pub Date : 2023-10-27DOI: 10.1080/01630563.2023.2267352
H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay
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).
{"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}
Pub Date : 2023-10-18DOI: 10.1080/01630563.2023.2267294
Deepesh Kumar Patel, Bhupeshwar Patel
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.
{"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}
Pub Date : 2023-10-17DOI: 10.1080/01630563.2023.2262828
Akram Chahid Bagy, Zaki Chbani, Hassan Riahi
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
{"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}
Pub Date : 2023-10-13DOI: 10.1080/01630563.2023.2266762
Alfredo N. Iusem, R. T. Marcavillaca
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
{"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}
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