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DOI: 10.23952/cot.2026.29
Received February 7, 2025; Accepted April 22, 2025; Published online March 13, 2026
Abstract. In this paper, we investigate optimality conditions for minimax problems using a dynamic programming approach. We present original results on necessary and sufficient optimality conditions for a broad class of problems, covering both finite and infinite set of parameters. Initially, we derive necessary optimality conditions for the case of finite parameters. Subsequently, we extend these results to the case of an uncountable number of parameters through a rigorous convergence analysis. The proofs of the main results are presented in detail. In addition to necessary conditions, we also explore sufficient optimality conditions and analyze the properties of the value function associated with the minimax problem. Our results contribute significantly to the theory of optimal control and have broad applications in fields like economics, engineering, and computer science.
How to Cite this Article:
P. G. Patzi Aquino, G. N. Silva, Dynamic programming approach for minimax control problems and optimality conditions, Commun. Optim. Theory 2026 (2026) 29.