Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches

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• 作者：Gabriele Eichfelder ; Maria Pilecka
• 关键词：Set optimization ; Set relation ; Variable ordering structure ; Scalarization
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：171
• 期：3
• 页码：947-963
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：171

文摘

This paper combines variable ordering structures with set relations in set optimization. We continue our examinations of set optimization problems and use the optimality notions as well as the set relations introduced in the paper (Eichfelder and Pilecka in Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach, 2016). We present linear scalarization results and a new nonlinear scalarization approach for set relations. Moreover, we introduce some additional set relations which allow us to investigate connections between our results, based on the set approach, and others presented in the literature which are based on the vector approach. This gives us the possibility to apply the optimality conditions derived there to our concepts.