Pub Date : 1900-01-01DOI: 10.23952/jano.4.2022.2.05
{"title":"Point-to-set distance functions for output-constrained neural networks","authors":"","doi":"10.23952/jano.4.2022.2.05","DOIUrl":"https://doi.org/10.23952/jano.4.2022.2.05","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"13 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":"117331071","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.1.03
W. Cholamjiak, S. Suantai, R. Suparatulatorn, S. Kesornprom, P. Cholamjiak
In this paper, we investigate the existence of fixed points for G-nonexpansive mappings and prove strong convergence theorems of a sequence generated by two different viscosity approximation methods for finding fixed points of these mappings in a Hilbert space with a directed graph. We also give examples and numerical results to support our main convergence theorem.
{"title":"Viscosity approximation methods for fixed point problems in Hilbert spaces endowed with graphs","authors":"W. Cholamjiak, S. Suantai, R. Suparatulatorn, S. Kesornprom, P. Cholamjiak","doi":"10.23952/jano.1.2019.1.03","DOIUrl":"https://doi.org/10.23952/jano.1.2019.1.03","url":null,"abstract":"In this paper, we investigate the existence of fixed points for G-nonexpansive mappings and prove strong convergence theorems of a sequence generated by two different viscosity approximation methods for finding fixed points of these mappings in a Hilbert space with a directed graph. We also give examples and numerical results to support our main convergence theorem.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"8 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":"128865420","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.1.04
L. Q. Anh, T. Bantaojai, N. P. Duc, T. Q. Duy, R. Wangkeeree, Alongkorn Rajabhat
This article deals with lexicographic equilibrium problems on Banach spaces. We first study the existence of solutions for such problems. Then, we investigate the Painlevé-Kuratowski convergence of the solution sets for a family of perturbed problems in a such way that they are perturbed by sequences constrained sets and objective functions converging. Several illustrative examples are given which clarify the essentialness of imposed assumptions. As an application, we discuss various results on the Painlevé-Kuratowski convergence for lexicographic variational inequalities.
{"title":"Convergence of solutions to lexicographic equilibrium problems","authors":"L. Q. Anh, T. Bantaojai, N. P. Duc, T. Q. Duy, R. Wangkeeree, Alongkorn Rajabhat","doi":"10.23952/jano.1.2019.1.04","DOIUrl":"https://doi.org/10.23952/jano.1.2019.1.04","url":null,"abstract":"This article deals with lexicographic equilibrium problems on Banach spaces. We first study the existence of solutions for such problems. Then, we investigate the Painlevé-Kuratowski convergence of the solution sets for a family of perturbed problems in a such way that they are perturbed by sequences constrained sets and objective functions converging. Several illustrative examples are given which clarify the essentialness of imposed assumptions. As an application, we discuss various results on the Painlevé-Kuratowski convergence for lexicographic variational inequalities.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"77 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":"125316937","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.4.2022.1.05
{"title":"A new class of vector optimization problems with linear fractional objective criteria","authors":"","doi":"10.23952/jano.4.2022.1.05","DOIUrl":"https://doi.org/10.23952/jano.4.2022.1.05","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"18 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":"125684805","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.2.01
{"title":"A special issue dedicated to Boris Polyak","authors":"","doi":"10.23952/jano.1.2019.2.01","DOIUrl":"https://doi.org/10.23952/jano.1.2019.2.01","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"30 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":"127431135","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.3.08
Jana Thomann, G. Eichfelder, G. Eichfelder
Optimization problems with multiple objectives which are expensive, i. e., where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance, analytically given, this can be used in the optimization procedure. Using a trust-region approach and the Tammer-Weidner-functional for finding descent directions, in [19] an algorithm was proposed which makes use of the heterogeneity of the objective functions. In this paper, we present three heuristic approaches, which allow to find additional optimal solutions of the multiobjective optimization problem and by that representations at least of parts of the Pareto front. We present the related theoretical results as well as numerical results on some test instances.
{"title":"Representation of the Pareto front for heterogeneous multi-objective optimization","authors":"Jana Thomann, G. Eichfelder, G. Eichfelder","doi":"10.23952/jano.1.2019.3.08","DOIUrl":"https://doi.org/10.23952/jano.1.2019.3.08","url":null,"abstract":"Optimization problems with multiple objectives which are expensive, i. e., where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance, analytically given, this can be used in the optimization procedure. Using a trust-region approach and the Tammer-Weidner-functional for finding descent directions, in [19] an algorithm was proposed which makes use of the heterogeneity of the objective functions. In this paper, we present three heuristic approaches, which allow to find additional optimal solutions of the multiobjective optimization problem and by that representations at least of parts of the Pareto front. We present the related theoretical results as well as numerical results on some test instances.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"21 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":"127841011","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.3.04
Andreas Löhne, D. Dörfler, Alexandra Rittmann, Benjamin Weißing
. In this paper, we study the relationship between bilevel programmes and polyhedral projection problems. Extending a well-known result by F¨ul¨op, we show that solving a bilevel problem with polyhedral constraints is equivalent to optimise the upper level objective over certain facets of an associated polyhedral projection problem. Utilising this result, we show how solutions to such bilevel problems can be computed.
{"title":"Solving bilevel problems with polyhedral constraint set","authors":"Andreas Löhne, D. Dörfler, Alexandra Rittmann, Benjamin Weißing","doi":"10.23952/jano.1.2019.3.04","DOIUrl":"https://doi.org/10.23952/jano.1.2019.3.04","url":null,"abstract":". In this paper, we study the relationship between bilevel programmes and polyhedral projection problems. Extending a well-known result by F¨ul¨op, we show that solving a bilevel problem with polyhedral constraints is equivalent to optimise the upper level objective over certain facets of an associated polyhedral projection problem. Utilising this result, we show how solutions to such bilevel problems can be computed.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"321 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":"132482751","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.3.07
L. Tung, T. Khai, P. T. Hung, P. Ngọc
In this paper, we consider set optimization problems with mixed constraints. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for strict minimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.
{"title":"Karush-Kuhn-Tucker optimality conditions and duality for set optimization problems with mixed constraints","authors":"L. Tung, T. Khai, P. T. Hung, P. Ngọc","doi":"10.23952/jano.1.2019.3.07","DOIUrl":"https://doi.org/10.23952/jano.1.2019.3.07","url":null,"abstract":"In this paper, we consider set optimization problems with mixed constraints. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for strict minimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"22 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":"114084109","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.1.2019.1.06
L. Tung, L. Tung
In this paper, a nonsmooth multiobjective semidefinite and semi-infinite programming is investigated. By using tangential subdifferentials for the tangential convex functions defined on the space of symmetric matrices, we establish the necessary and sufficient optimality conditions for some kind of efficient solutions of the nonsmooth multiobjective semidefinite and semi-infinite programming.
{"title":"Karush-Kuhn-Tucker optimality conditions for nonsmooth multiobjective semidefinite and semi-infinite programming","authors":"L. Tung, L. Tung","doi":"10.23952/jano.1.2019.1.06","DOIUrl":"https://doi.org/10.23952/jano.1.2019.1.06","url":null,"abstract":"In this paper, a nonsmooth multiobjective semidefinite and semi-infinite programming is investigated. By using tangential subdifferentials for the tangential convex functions defined on the space of symmetric matrices, we establish the necessary and sufficient optimality conditions for some kind of efficient solutions of the nonsmooth multiobjective semidefinite and semi-infinite programming.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"26 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":"125430623","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}
Pub Date : 1900-01-01DOI: 10.23952/jano.2.2020.3.01
C. Izuchukwu, Y. Shehu
In solving variational inequalities, the inertial extrapolation step is a highly powerful tool in algorithmic designs and analyses mainly due to the improved convergence speed that it contributes to the algorithms. However, it has been discovered that the presence of the inertial extrapolation steps in these methods for solving variational inequalities makes them lose some of their attractive properties, for example, the Fejér monotonicity (with respect to the solution set) of the sequence generated by projection-type methods for solving variational inequalities is lost when the iterative steps involve an inertial term, which makes these methods sometimes not converge faster than the corresponding algorithms without an inertial term. To avoid such a situation, we present two new projection-type methods with alternated inertial extrapolation steps for solving multivalued variational inequality problems, which inherit the Fejér monotonicity property of the projection-type method to some extent. Furthermore, we prove the convergence of the sequence generated by our methods under much relaxed assumptions on the inertial extrapolation factor and the multivalued mapping associated with the problem. Moreover, we establish the convergence rate of our methods and provide several numerical experiments of the new methods in comparison with other related methods in the literature.
{"title":"Projection-type methods with alternating inertial steps for solving multivalued variational inequalities beyond monotonicity","authors":"C. Izuchukwu, Y. Shehu","doi":"10.23952/jano.2.2020.3.01","DOIUrl":"https://doi.org/10.23952/jano.2.2020.3.01","url":null,"abstract":"In solving variational inequalities, the inertial extrapolation step is a highly powerful tool in algorithmic designs and analyses mainly due to the improved convergence speed that it contributes to the algorithms. However, it has been discovered that the presence of the inertial extrapolation steps in these methods for solving variational inequalities makes them lose some of their attractive properties, for example, the Fejér monotonicity (with respect to the solution set) of the sequence generated by projection-type methods for solving variational inequalities is lost when the iterative steps involve an inertial term, which makes these methods sometimes not converge faster than the corresponding algorithms without an inertial term. To avoid such a situation, we present two new projection-type methods with alternated inertial extrapolation steps for solving multivalued variational inequality problems, which inherit the Fejér monotonicity property of the projection-type method to some extent. Furthermore, we prove the convergence of the sequence generated by our methods under much relaxed assumptions on the inertial extrapolation factor and the multivalued mapping associated with the problem. Moreover, we establish the convergence rate of our methods and provide several numerical experiments of the new methods in comparison with other related methods in the literature.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"116 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":"124794582","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}
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