Minimax Control Problems: Optimality Conditions

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every M...

Sufficient Optimality Conditions for Multivariable Control Problems

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state – by assuming weak hypotheses) constraints.

Optimality Conditions for Unconstrained Problems

Optimality conditions for multidimensional control problems with polyconvex gradient restrictions

The motivation for a closer investigation of Dieudonné-Rashevsky type problems (P) is two-fold. First, due to its close affinity to the basic problem of multidimensional calculus of variations, the problem (1.3) − (1.5) is well-suited as a model problem in order to ascertain how the proof of optimality conditions is influenced through the weakening of the convexity properties of the data. Since...

Optimality Conditions for Nonconvex Multistate Control Problems in the Coefficients

The purpose of this paper is to attain some optimality conditions for the identification of a diffusion matrix (material) under several restrictions. Assuming that the set of such diffusion matrices is closed for the H-convergence, we give a method to obtain admissible directions which applies to a not-necessarily convex control set. Our results permit obtaining the diffusion matrix from the st...