CONDITIONS OF HIGH ORDER FOR A LOCAL MINIMUM IN PROBLEMS WITH CONSTRAINTS

Abstract

CONTENTS Introduction Chapter I. The apparatus § 1. Convex analysis § 2. Approximations Chapter II. The family of functions ; the main conditions for a local minimum § 3. The problem of a conditional extremum and related concepts § 4. The main necessary condition for a local minimum § 5. The theorem about the estimation of the distance to the solution set of a system of strict non-linear inequalities and of an operator equation § 6. The main sufficient condition for a local minimum Chapter III. Conditions of order γ § 7. Necessary conditions of order γ § 8. Sufficient conditions of order γ Chapter IV. The family of functions § 9. Conditions for the equivalence of the families and § 10. A smooth system S Chapter V. Theory of a minimum on a set of sequences § 11. Main concepts and theorems of the general theory Chapter VI. Quadratic conditions for a minimum in various classes of extremal problems § 12. A smooth problem in Rn § 13. The problem of Bliss with end inequalities § 14. A vector optimization problem with a continuum of cost functions Supplement to Chapter VI Comments References