Tilt扰动下的稳定全局极小值

Stable Global Minima under Tilt Perturbations

摘要: 当Ψ，φ是admissible函数时，我们考虑了集值映射的全局Ψ-开性，证明了其与全局Ψ-度量正则性是等价的。我们把φ-正则函数的定义拓展至全局情形，证明了全空间上的φ-仿凸函数是连续全局φ-正则的。在目标函数是连续全局φ-正则的或φ-仿凸的假定下，我们研究了tilt扰动下的稳定全局极小值与目标函数次微分的全局度量正则性之间的关系，将一些已有的凸性结果推广至非凸情形。

Abstract: When Ψ,φ are admissible functions, we consider the global Ψ-openness of the set-valued map and show that it is equivalent to the global Ψ-metric regularity. We extend the definition of φ-regular functions to the global case, and prove that the φ-paraconvex function on the whole space is continuously globally φ-regular. Under the assumption that the objective function is continuously globally φ-regular or φ-paraconvex, we study the relationship between the stable global minimum and the global metric regularity of the subdifferential of the objective function under tilt perturbations, and extend some convexity results to non-convex cases.