Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems
研究了一类参数集优化问题的解稳定性和适定性，给出了解映射外连续性、外开性和内开性的充分条件，并利用锥连续性推导了Levitin-Polyak适定性和Hadamard适定性条件。
Abstract This paper investigates the solution stability and well-posedness for a parametric set optimization problem (PSOP), where lower and upper set order relations are induced by an improvement set. We provide new sufficient conditions for the outer-continuity, outer-openness and inner-openness of the solution mapping of (PSOP). By utilizing the property of cone-continuity, we derive sufficient conditions ensuring the Levitin-Polyak well-posedness for (PSOP) and the Hadamard well-posedness for a related parametric implicit set optimization problem (ISOP). Numerical examples are also given to illustrate the main results.