An algorithm for solving linearly constrained minimax problems

In this study, we propose an algorithm for solving a minimax problem over a polyhedral set defined in terms of a system of linear inequalities. At each iteration a direction is found by solving a quadratic programming problem and then a suitable step size along that direction is taken through an extension of Armijo's approximate line search technique. We show that each accumulation point is a Kuhn-Tucker solution and give a condition that guarantees convergence of the whole sequence of iterations. Through the use of an exact penalty function, the algorithm can be used for solving constrained nonlinear programming. In this case, our algorithm resembles that of Han, but differs from it both in the direction-finding and the line search steps.