A quasimonotonic max-min programming problem with linked linear contraints. (English) Zbl 0611.49005

The paper is concerned with a max-min problem having a quasimonotonic objective function and linear constraints. This problem represents a generalization of some max-min problems considered in the literature in which the objective function was assumed to be linear or linear- fractional. We generalize in the quasimonotonic case a number of results obtained for the linear and linear-fractional max-min problems. It is shown that the quasimonotonic max-min problem can be reduced to a quasiconvex programming problem having at least an optimal solution which is a vertex of the feasible set. A finite algorithm for solving this problem is suggested.


49J35 Existence of solutions for minimax problems
90C55 Methods of successive quadratic programming type
90C25 Convex programming
65K05 Numerical mathematical programming methods