Duality in fractional minimax programming

1. IntroductionThe study of minimax optimization problems has been of considerable interest in thepast-—see for example [7] and [8], and the references cited therein. Schmitendrof [14]considered a very general class of static minimax problems and presented neces-sary/sufficient optimality conditions for the same. Later, Tanimoto [15] constructed adual to the problem studied by Schmitendrof [14 an] d proved various duality theoremsunder convexity assumptions on objective and constraint functions. Recently, Yadavand Mukherjee [16] attempted to construct a dual to the fractional analogue of theproblem considered by Tanimoto [15] and presented a duality theorem similar to theone given in [15].The purpose of this paper is to point out certain omissions and inconsistencies in thework reported in [16] and to present two modified models of the dual for the fractionalminimax problem considered there. These models have been motivated by those dueto Mond and Weir [11] for scalar fractional programming and Bector et alia [2] forgeneralized fractional programming problems.This paper has been divided into four sections. Section 2 includes preliminaries