Penalty Function Interval Method for Solving Constrained Continuous Minimax Problem

A numerical method was studied to solve constrained continuous minimax problems with a Lipschitz continuous objective function and constrained functions. The penalty function method was built to transform a constrained continuous minimax algorithm into a bi-level programming problem, and the convergence of the algorithm was proved. At last, the unconstrained bi-level programming interval algorithm was applied to solve the problem, and numerical examples were given to show the efficiency and the reliability of this algorithm.