A Power Method to Convex-Concave Minmax Optimization Problems with Nonlinear Constraints

In this paper, we presents a new power penalty method to convex-concave minimax optimization problems with nonlinear constraints. This method first reformulate the KKT conditions of such optimization problem approximated by a nonlinear equation containing a power penalty term. Then we will show that the solution of the penalty equation converges to that of the mixed complementarity problem at an exponential rate, which is depending on the parameters in the penalty equation, and some numerical results are presented to verify the theoretical results.