@Article{JCM-10-305,
author = {Goong Chen and Quan Zheng},
title = {Minimax Methods for Open-Loop Equilibra in $N$-Person Differential Games Part II: Duality and Penalty Theory},
journal = {Journal of Computational Mathematics},
year = {1992},
volume = {10},
number = {4},
pages = {305--320},
abstract = {<p style="text-align: justify;">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. <br/>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. <br/>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.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9364.html}
}