On Generalized Semi-Infinite Optimization Problems
by
Jan-J. Rückmann
Technische Universität Ilmenau, Institut für Mathematik, PF 100565, D-98684 Ilmenau, Germany
Coauthors: Alexander Shapiro (Atlanta)

We consider generalized semi-infinite optimization problems whose feasible sets are defined by infinitely many real-valued inequality constraints and the index sets of the constraints depend (additionally) on the finite-dimensional vector of the state variables. We analyze topological properties of the feasible set and show their relationship to first and second order necessary and sufficient conditions for the underlying problem. First order conditions are obtained by using three different approaches: a Fritz-John-Type Theorem, conditions based on linearizations of the describing functions and conditions using the calculus of quasidifferentiable functions. Necessary and sufficient second order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is second order (parabolically) directionally differentiable and second order epiregular at the considered point. These sufficient conditions are, in particular, equivalent to the second order growth condition. The lecture is based on recent joint papers with Alexander Shapiro (Atlanta).

Key Words: Generalized semi-infinite optimization, topological structure of the feasible set, first and second order optimality conditions, optimal value function

Date received: April 23, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahh-10.