An active-set algorithm and a trust-region approach in constrained minimax problem

In this paper, we propose an algorithm to solve a finite minimax problem with side constraints. An active-set strategy is used in the algorithm to transform inequality constraints to equality constraints. This allows the use of the well-developed techniques for solving the equality constrained optimization problems. A trust-region globalization strategy is added to the proposed algorithm to ensure global convergence. A projected Hessian technique is used in the algorithm to overcome the difficulty of having an infeasible trust-region subproblem. A global convergence theory for the proposed algorithm is presented under standard assumptions. Finally, numerical experiments are reported to indicate that the new algorithm performs efficiently in practice.