Optimality Conditions for Nonregular Optimal Control Problems and Duality

ABSTRACT

We define a new class of optimal control problems and show that this class is the largest one of control problems where every admissible process that satisfies the Extended Pontryaguin Maximum Principle is an optimal solution of nonregular optimal control problems. In this class of problems the local and global minimum coincide. A dual problem is also proposed, which may be seen as a generalization of the Mond–Weir-type dual problem, and it is shown that the 2-invexity notion is a necessary and sufficient condition to establish weak, strong, and converse duality results between a nonregular optimal control problem and its dual problem. We also present an example to illustrate our results.

KEYWORDS:

• Control problem
• nonregular problems
• optimality condition

MATHEMATICS SUBJECT CLASSIFICATION:

• 34H05
• 49N15
• 49K15

Acknowledgment

The authors greatly appreciate the anonymous referee for their useful comments and suggestions, which have helped to improve an early version of the paper.