Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: OPTIMIZATION OF DISCRETE AND DIFFERENTIAL INCLUSIONS OF GOURSAT-DARBOUX TYPE WITH STATE CONSTRAINTS | OPTIMIZATION OF DISCRETE AND DIFFERENTIAL INCLUSIONS OF GOURSAT-DARBOUX TYPE WITH STATE CONSTRAINTS ELIMHAN N. MAHMUDOV Received 14 October 2005 Revised 11 September 2006 Accepted 20 September 2006 Necessary and sufficient conditions of optimality under the most general assumptions are deduced for the considered and for discrete approximation problems. Formulation of sufficient conditions for differential inclusions is based on proved theorems of equivalence of locally conjugate mappings. Copyright 2006 Elimhan N. Mahmudov. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In the last decade discrete and continuous time processes with lumped and distributed parameters found wide application in the field of mathematical economics and in problems of control dynamic system optimization and differential games 1-19 . The present article is devoted to an investigation of problems of this kind with distributed parameters where the treatment is in finite-dimensional Euclidean spaces. It can be divided conditionally into four parts. In the first part Section 2 a certain extremal problem is formulated for discrete inclusions of Goursat-Darboux type. For such problems we use constructions of convex and nonsmooth analysis in terms of convex upper approximations local tents and locally conjugate mappings for both convex and for nonconvex problems to get necessary and sufficient conditions for optimality. In the third part Section 4 we use difference approximations of derivatives and grid functions on a uniform grid to approximate the problem with differential inclusions of Goursat-Darboux type and to formulate a necessary and sufficient condition for optimality for the discrete approximation problem. It is obvious that such difference problems can play an important role also in computational procedures.
