In this article, concepts of metrically pointwise and metrically global Levitin-Polyak (LP) well-posed parametric set optimization problems are introduced. Characterizations of metrically pointwise and metrically glob...
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In this article, concepts of metrically pointwise and metrically global Levitin-Polyak (LP) well-posed parametric set optimization problems are introduced. Characterizations of metrically pointwise and metrically global LP well-posed parametric set optimization problems are scrutinized in detail. Connections between metrically pointwise LP well-posed parametric set optimization problems and a approximate solution map are established. Connections between metrically global LP well-posed parametric set optimization problems and the approximate solution map are also established. The role of upper semicontinuity and compactness of the approximate solution map are also analysed for a parametric set optimization problem to be metrically pointwise and global LP well-posed. The role of excess function in the approximate solution map is also scrutinized for a parametric set optimization problem to be metrically pointwise LP well-posed. Relationships between pointwise LP well-posedness and metrically pointwise LP well-posedness are derived. Relationships between global LP well-poseness and metrically global LP well-posedness are also analysed. All the links are properly established to prove the necessary and sufficient conditions.
In this paper, we establish the upper, lower semicontinuity and closedness of the minimal solution and weak minimal solution set mappings to a parametricset-valued vector optimizationproblem with setoptimization cr...
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In this paper, we establish the upper, lower semicontinuity and closedness of the minimal solution and weak minimal solution set mappings to a parametricset-valued vector optimizationproblem with setoptimization criterion under some suitable assumptions.
In this paper, we establish the upper semi-continuity, lower semi-continuity and compactness of relaxed minimal and minimal solution mappings for parametric set optimization problems, where the objective set-valued ma...
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In this paper, we establish the upper semi-continuity, lower semi-continuity and compactness of relaxed minimal and minimal solution mappings for parametric set optimization problems, where the objective set-valued mappings take values in the topological space introduced by Geoffroy [A topological convergence on power sets well-suited for setoptimization. J Global Optim. 2019;73:567-581].
setoptimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on th...
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setoptimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on the continuity of the strict (weak) minimal solution set mapping of parametricset-valued vector optimizationproblems with the lower set less order relation. We firstly introduce a concept of strict lower level mapping of parametricset-valued vector optimizationproblems. Moreover, the upper and lower semicontinuity of the strict lower level mapping are obtained under some suitable conditions. Lastly, the sufficient condition for the continuity of the strict minimal solution set mappings of parametric set optimization problems are established by a new proof method, which is different from that in [27, 28].
This paper mainly investigates the semicontinuity of solution mappings for setoptimizationproblems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two ...
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This paper mainly investigates the semicontinuity of solution mappings for setoptimizationproblems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
The aim of this paper is to investigate the stability of the solution sets for setoptimizationproblems via improvement sets. Firstly, we consider the relations among the solution sets for optimizationproblem with s...
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The aim of this paper is to investigate the stability of the solution sets for setoptimizationproblems via improvement sets. Firstly, we consider the relations among the solution sets for optimizationproblem with setoptimization criterion. Then, the closeness and the convexity of solution sets are discussed. Furthermore, the upper semi-continuity, Hausdorff upper semi-continuity and lower semi-continuity of solution mappings to parametric set optimization problems via improvement sets are established under some suitable conditions. These results extend and develop some recent works in this field.
In this paper we study the stability of the minimal solutions of setoptimizationproblems. We provide sufficient conditions for the upper and lower semicontinuity and compactness of the minimal solutions of parametri...
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In this paper we study the stability of the minimal solutions of setoptimizationproblems. We provide sufficient conditions for the upper and lower semicontinuity and compactness of the minimal solutions of parametric set optimization problems whose objective values are not necessarily compact.
The aim of this paper is to investigate the continuity of the solution set maps of set-valued vector optimizationproblems with setoptimization criterion. First, we introduce a new concept, which is called a u-lower ...
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The aim of this paper is to investigate the continuity of the solution set maps of set-valued vector optimizationproblems with setoptimization criterion. First, we introduce a new concept, which is called a u-lower level map. Then, we give some sufficient conditions for the upper and lower semicontinuities of the generalized lower level map. Finally, by virtue of the semicontinuity of the u-lower level map, we obtain the continuity of the minimal solution set map to parametricset-valued vector optimizationproblems with setoptimization criterion.
In this paper,under some suitable assumptions without any involving information on the solution set,we give some sufficient conditions for the upper semicontinuity,lower semicontinuity,and closedness of the solution s...
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In this paper,under some suitable assumptions without any involving information on the solution set,we give some sufficient conditions for the upper semicontinuity,lower semicontinuity,and closedness of the solution set mapping to a parametric set optimization problem with possible less order relation.
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