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.1.2019.2.05
A. Gibali, HA NGUYENH., N. T. Thuong, T. H. Trang, N. T. Vinh
In this paper, we are concerned with the problem of finding minimum-norm solutions of a split convex feasibility problem in real Hilbert spaces. We study and analyze the convergence of a new self-adaptive CQ algorithm. The main advantage of the algorithm is that there is no need to calculate the norm of the involved operator.
{"title":"Polyak’s gradient method for solving the split convex feasibility problem and its applications","authors":"A. Gibali, HA NGUYENH., N. T. Thuong, T. H. Trang, N. T. Vinh","doi":"10.23952/jano.1.2019.2.05","DOIUrl":"https://doi.org/10.23952/jano.1.2019.2.05","url":null,"abstract":"In this paper, we are concerned with the problem of finding minimum-norm solutions of a split convex feasibility problem in real Hilbert spaces. We study and analyze the convergence of a new self-adaptive CQ algorithm. The main advantage of the algorithm is that there is no need to calculate the norm of the involved operator.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"33 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":"125698635","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.1.2019.2.01
{"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.2.2020.2.02
Li Xiao-huan, Q. Dong, A. Gibali
In this paper, we introduce some new iterative algorithms for finding fixed points of nonexpansive mappings with the aid of projection and contraction methods. Weak and strong convergence theorems are established under mild conditions in Hilbert spaces. The numerical examples are presented to illustrate the advantage of our proposed algorithms.
{"title":"Some new iterative algorithms for finding fixed points of nonexpansive mappings","authors":"Li Xiao-huan, Q. Dong, A. Gibali","doi":"10.23952/jano.2.2020.2.02","DOIUrl":"https://doi.org/10.23952/jano.2.2020.2.02","url":null,"abstract":"In this paper, we introduce some new iterative algorithms for finding fixed points of nonexpansive mappings with the aid of projection and contraction methods. Weak and strong convergence theorems are established under mild conditions in Hilbert spaces. The numerical examples are presented to illustrate the advantage of our proposed algorithms.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"36 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":"133755566","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.1.2019.2.08
Gayatri Pany, O. Chadli, R. Mohapatra, R. Mohapatra
In this paper, we study a class of mixed equilibrium problems under the extended generalized α–η monotonicity in finitely continuous topological spaces. Existence of solutions to the problems is established by relaxing the convexity structure and the linearity condition by using the relatively Knaster-Kuratowski-Mazurkiewicz principle. We also propose an iterative scheme based on auxiliary principle techniques. The results obtained in this paper improve and generalize some recent results in the framework of FC spaces under weaker conditions. They are useful to solve problems, where the domain and range of the underlying mappings lack the convexity structure.
{"title":"Generalized monotone mixed equilibrium problems in FC-spaces: Existence and approximation","authors":"Gayatri Pany, O. Chadli, R. Mohapatra, R. Mohapatra","doi":"10.23952/jano.1.2019.2.08","DOIUrl":"https://doi.org/10.23952/jano.1.2019.2.08","url":null,"abstract":"In this paper, we study a class of mixed equilibrium problems under the extended generalized α–η monotonicity in finitely continuous topological spaces. Existence of solutions to the problems is established by relaxing the convexity structure and the linearity condition by using the relatively Knaster-Kuratowski-Mazurkiewicz principle. We also propose an iterative scheme based on auxiliary principle techniques. The results obtained in this paper improve and generalize some recent results in the framework of FC spaces under weaker conditions. They are useful to solve problems, where the domain and range of the underlying mappings lack the convexity structure.","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":"117246109","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：