A Necessary Condition for a Terminal Point Problem Governed by a Discrete Inclusion System

Abstract

In this talk we will give a necessary condition for K-optimality of the following Mayer type optimization problem min x_T x_{t+1} ∈ F_t(x_t), t = 0, ..., T − 1 x_0 ∈ M where T ∈ N, the F_t : X_t → X_{t+1}, t = 0, ..., T − 1, are Lipschitzian set-valued mappings in neighborhoods of the points x_t, t = 0, ..., T − 1 respectively, the X_t, t = 0, ..., T, are finite-dimensional Euclidean spaces, and M ⊂ X_0. We also assume that the space X_T is partially ordered by a proper cone K.