Stability and Sensitivity Analysis

Abstract

In this chapter we study parameterized optimization problems of the form

$$({P_u})\mathop {Min}\limits_{x \in X} f(xu)subjecttoG(xu) \in K$$

(4.1)

, depending on the parameter vector u ∈ U. Unless stated otherwise we assume in this chapter that X, Y, and U are Banach spaces, K is a closed convex subset of Y, and f : X × U → IR and G : X × U → Y are continuous. In some situations we deal with minimization of f(·, u) over an abstract set Φ(u) ⊂ X. In any case we denote by Φ(u) the feasible set of the current optimization problem.