Abstract

We propose definitions of well-posedness under perturbation in terms of suitable asymptotically solving sequences, not embedding a given problem into a parameterized family. When considering in detail quasi-equilibrium and quasi-optimization problems as well as optimization problems with equilibrium constraints, we establish sufficient conditions for both well-posedness and unique well-posedness. For cases with noncompact underlying sets of constraints, measures of noncompactness are employed. We provide numerous examples to ensure the essentialness of the assumptions imposed in the obtained results.

中文翻译：

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关于微扰拟平衡和拟优化问题的适定性

摘要

我们根据合适的渐近求解序列提出了扰动下适定性的定义，而不是将给定问题嵌入到参数化族中。在详细考虑拟平衡和拟优化问题以及具有平衡约束的优化问题时，我们为适定性和唯一适定性都建立了充分条件。对于具有非紧凑基础约束集的情况，采用非紧凑性度量。我们提供了许多示例以确保在获得的结果中强加的假设的必要性。