On a quasimonotonic max-min problem. (English) Zbl 0727.90062

Ţigan, Ştefan

Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 19, No. 1, 85-91 (1990).

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, linear-fractional or polynomial linear-fractional. It is shown that a 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.

MSC:

90C26	Nonconvex programming, global optimization
90-08	Computational methods for problems pertaining to operations research and mathematical programming

Keywords:

max-min problem; quasimonotonic objective function; linear constraints; quasiconvex programming