MATHEMATICAL PROGRAMMING AND POLYHEDRAL OPTIMIZATION OF SECOND ORDER DISCRETE AND DIFFERENTIAL INCLUSIONS

The present paper is devoted to a difficult and interesting field-second order polyhedral optimization described by ordinary discrete and differential inclusions. The posed problems and the corresponding optimality conditions are new. The stated second order discrete problem is reduced to the polyhedral minimization problem with polyhedral geometric constraints and in terms of the polyhedral Euler-Lagrange inclusions, necessary and sufficient conditions for optimality are derived. Derivation of the sufficient conditions for the second order polyhedral differential inclusions is based on the discrete-approximation method. The transversality condition is formulated separately, a fact peculiar to problems involving higher order derivatives.