Optimization of boundary value problems for higher order differential inclusions and duality

Abstract

A duality theory for boundary value problems for differential inclusions of higher orders is proposed by means of locally conjugate mappings in the form of Euler-Lagrange type inclusions and transversality conditions. Sufficient optimality conditions are derived, too. To illustrate the proposed approach, third-order semilinear boundary value problems and polyhedral fourth-order boundary value problems are considered, and extensions towards problems of any order are discussed.