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Approximate Solutions and Levitin–Polyak Well-Posedness for Set Optimization Using Weak Efficiency
Journal of Optimization Theory and Applications ( IF 1.9 ) Pub Date : 2020-06-17 , DOI: 10.1007/s10957-020-01683-0 Meenakshi Gupta , Manjari Srivastava
Journal of Optimization Theory and Applications ( IF 1.9 ) Pub Date : 2020-06-17 , DOI: 10.1007/s10957-020-01683-0 Meenakshi Gupta , Manjari Srivastava
The present study is devoted to define a new notion of approximate weak minimal solution based on a set order relation introduced by Karaman et al. (Positivity 22(3):783–802, 2018) for a constrained set optimization problem. Sufficient conditions have been found for the closedness of minimal solution sets. Using the Painlevé–Kuratowski convergence, the stability aspects of the approximate weak minimal solution sets are discussed. Further, a notion of Levitin–Polyak well-posedness for the set optimization problem is introduced. Sufficiency criteria and some characterizations of the above defined well-posedness are established. An alternative approach to obtain robust solutions for uncertain vector optimization problems is discussed as an application.
中文翻译:
使用弱效率的集合优化的近似解和 Levitin-Polyak 适定性
本研究致力于基于 Karaman 等人引入的集合顺序关系定义近似弱最小解的新概念。(Positivity 22(3):783–802, 2018)用于约束集优化问题。已经找到了最小解集的封闭性的充分条件。使用 Painlevé-Kuratowski 收敛,讨论了近似弱最小解集的稳定性方面。此外,还引入了用于集合优化问题的 Levitin-Polyak 适定性的概念。建立了上述定义的适定性的充分性标准和一些特征。作为应用程序讨论了获得不确定向量优化问题的稳健解决方案的替代方法。
更新日期:2020-06-17
中文翻译:
使用弱效率的集合优化的近似解和 Levitin-Polyak 适定性
本研究致力于基于 Karaman 等人引入的集合顺序关系定义近似弱最小解的新概念。(Positivity 22(3):783–802, 2018)用于约束集优化问题。已经找到了最小解集的封闭性的充分条件。使用 Painlevé-Kuratowski 收敛,讨论了近似弱最小解集的稳定性方面。此外,还引入了用于集合优化问题的 Levitin-Polyak 适定性的概念。建立了上述定义的适定性的充分性标准和一些特征。作为应用程序讨论了获得不确定向量优化问题的稳健解决方案的替代方法。