A Connection between the Adjoint Variables and Value Function for Differential Games

  • Rania Benmenni Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, University Ferhat Abbas Setif-1, Setif 19000, Algeria
  • Nourreddine Daili Department of Mathematics, Faculty of Sciences, University Ferhat Abbas Setif-1 , Setif 19000, Algeria
DOI: https://doi.org/10.19139/soic-2310-5070-2115
Keywords: Nonzero-sum differential games, Maximum principle, Dynamic programming principle, super- and subdifferentials.

Abstract

In this paper, we present a deterministic two-player nonzero-sumd ifferential games (NZSDGs) in a finite horizon. The connection between the adjoint varaibles in the maximum principle (MP) and the value function in the dynamic programming principle (DPP) for differentail games is obtained in either case, whether the value function is smooth and nonsmooth. For the smooth case, the connection between the adjoint variables and the derivatives of the value function are equal to each other along optimal trajectories. Furthermore, for the nonsmooth case, this relation is represented in terms of the adjoint variables and the first-order super- and subdifferentials of the value function. We give an example to illustrate the theoretical results.
Published
2024-08-19
How to Cite
Benmenni, R., & Daili, N. (2024). A Connection between the Adjoint Variables and Value Function for Differential Games. Statistics, Optimization & Information Computing, 13(1), 173-188. https://doi.org/10.19139/soic-2310-5070-2115
Issue
Vol 13 No 1 (2025)
Section
Research Articles
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