Conditions of High Order for a Local Minimum in Problems With Constraints

CONTENTSIntroductionChapter 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 ? ??7. Necessary conditions of order ? ??8. Sufficient conditions of order ?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