Abstract:

In this paper, a new objective penalty function approach is proposed for
solving minimax programming problems with equality and inequality constraints.
This new objective penalty function combines the objective penalty and constraint
penalty. By the new objective penalty function, a constrained minimax problem is
converted to minimizations of a sequence of continuously differentiable functions
with a simple box constraint. One can thus apply any efficient gradient minimization
methods to solve the minimizations with box constraint at each step of the sequence.
Some relationships between the original constrained minimax problem and the
corresponding minimization problems with box constraint are established. Based on
these results, an algorithm for finding a global solution of the constrained minimax
problems is proposed by integrating the particular structure of minimax problems
and its global convergence is proved under some conditions. Furthermore, an
algorithm is developed for finding a local solution of the constrained minimax of numerical experiments with well-known test problems show that satisfactorily
approximate solutions for some constrained minimax problems can be obtained.
problems, with its convergence proved under certain conditions. Preliminary results