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On Levitin–Polyak well-posedness and stability in set optimization
Positivity ( IF 1 ) Pub Date : 2021-07-13 , DOI: 10.1007/s11117-021-00849-y
Meenakshi Gupta 1 , Manjari Srivastava 2
Affiliation  

In this paper, Levitin–Polyak (in short LP) well-posedness in the set and scalar sense are defined for a set optimization problem and a relationship between them is found. Necessary and sufficiency criteria for the LP well-posedness in the set sense are established. Some characterizations in terms of Hausdorff upper semicontinuity and closedness of approximate solution maps for the LP well-posedness have been obtained. Further, a sequence of solution sets of scalar problems is shown to converge in the Painlevé–Kuratowski sense to the minimal solution sets of the set optimization problem. Finally, the perturbations of the ordering cone and the feasible set of the set optimization problem are considered and the convergence of its weak minimal and minimal solution sets in terms of Painlevé–Kuratowski convergence is discussed.



中文翻译:

集合优化中的 Levitin–Polyak 适定性和稳定性

在本文中,Levitin–Polyak(简称LP)在集合和标量意义上的适定性被定义为一个集合优化问题,并找到了它们之间的关系。建立了集合意义上的LP适定性的必要和充分条件。LP近似解映射的 Hausdorff 上半连续性和封闭性方面的一些表征已获得良好的姿势。此外,一系列标量问题的解集被证明在 Painlevé-Kuratowski 意义上收敛到集优化问题的最小解集。最后,考虑了排序锥的扰动和集合优化问题的可行集,并讨论了其弱最小和最小解集在Painlevé-Kuratowski收敛方面的收敛性。

更新日期:2021-07-13
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