Minimax Methods for Open-Loop Equilibra in $N$-Person Differential Games Part II: Duality and Penalty Theory
Year: 1992
Journal of Computational Mathematics, Vol. 10 (1992), Iss. 4 : pp. 305–320
Abstract
The equilibrium strategy for $N$-person differential games can be obtained from a min-max problem subject to differential constraints. The differential constraints are treated here by the duality and penalty methods.
We first formulate the duality theory. This involves the introduction of $N+1$ Lagrange multipliers: one for each player and one commonly shared by all players. The primal min-max problem thus results in a dual problem, which is a max-min problem with no differential constraints.
We develop the penalty theory by penalizing $N+1$ differential constraints. We give a convergence proof which generalizes a theorem due to B.T. Polyak.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1992-JCM-9364
Journal of Computational Mathematics, Vol. 10 (1992), Iss. 4 : pp. 305–320
Published online: 1992-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16