On duality in problems of optimal control described by convex differential inclusions of Goursat–Darboux type

Abstract

Sufficient conditions of optimality are derived for convex and non-convex problems with state constraints on the basis of the apparatus of locally conjugate mappings. The duality theorem is formulated and the conditions under which the direct and dual problems are connected by the duality relation are searched for.  2005 Elsevier Inc. All rights reserved.

Sufficient Conditions of Optimality for Convex Differential Inclusions of Elliptic Type and Duality

“…A lot of problems in economic dynamics, as well as classical problems on optimal control in vibrations, chemical engineering, heat, diffusion processes, differential games, and so on, can be reduced to such investigations with ordinary and partial differential inclusions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We refer the reader to the survey papers [11,[16][17][18][19][20]. The present paper is organized as follows.…”

“…It turn out that such form of optimality conditions automatically implies the Weierstrass-Pontryagin maximum condition. Apparently it happens because the LAM is more applicable apparat in different type of problems governed by differential inclusions [16][17][18][19][20].…”

“…It means that if some pair of feasible solutions (u(. ),u inclusions in [17][18][19]. Some duality relations and optimality conditions for an extremum of different control problems with partial differential inclusions can be found in [18,19].…”

Necessary and sufficient conditions for discrete and differential inclusions of elliptic type

“…Some duality relations and optimality conditions for an extremum of different control problems with partial differential inclusions can be found in [2,4,5,9,[17][18][19][20][21].…”

The optimality principle for discrete and first order partial differential inclusions

“…A great number of problems in economic dynamics, as well as classical problems on optimal control, differential games, and so on, can be reduced to such investigations [2][3][4][5][6][7][8][9][10][11][12].…”