TY - JOUR
T1 - Minimax Methods for Open-Loop Equilibra in $N$-Person Differential Games Part II: Duality and Penalty Theory
AU - Goong Chen & Quan Zheng
JO - Journal of Computational Mathematics
VL - 4
SP - 305
EP - 320
PY - 1992
DA - 1992/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9364.html
KW - 
AB - <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>