Abstract
This paper is concerned with an optimization-satisfaction problem to determine an optimal solution such that a certain objective function is minimized subject to satisfaction conditions against uncertainties of any opponents' decisions or disturbances. Such satisfaction conditions require that plural performance criteria are always less than specified values against any opponents' decisions or disturbances. Therefore, this problem is formulated as a minimization problem with the constraints which include max operations with respect to the opponents' decision variables. The most general class of those problems where the objective and constraint functions depend on the maximizers as well as the minimizers is studied. A new computational method is proposed such that a series of approximate problems transformed by applying a penalty function method to the max operations within the satisfaction condition are solved by usual nonlinear programming. It is proved that a sequence of approximated solutions converges to the true optimal solution. The proposed algorithm may be useful for the systems design under unknown parameters, the process control under uncertainties, the study of general approximation theory, the strategic weapon allocation program etc.
