Perturbation of Generalized Kuhn-Tucker Points in Finite-Dimensional Optimization

Abstract

A very large and versatile class of optimization problems can be posed in the form

$$\min imizef\left( x \right) + h\left( {F\left( x \right)} \right)overallx \in X$$

(P)

, where X is a nonempty polyhedral (convex) set in ℝⁿ, the mappings f : ℝⁿ → ℝ and F : ℝⁿ → ℝ^m are of class C ², and the function h : ℝ^m → ℝ is convex and possibly extended-real-valued, specifically of the form

$$h\left( u \right) = \sup \left\{ {yu - g\left( y \right)} \right\} = \left( {d + \delta Y} \right)*\left( u \right)$$

(1.1)

for a nonempty polyhedral (convex) set Y ⊂ ℝ^m and a convex function g : ℝ^m → ℝ of class C ².