Quasiconcavity and nondominated solutions in multiobjective programming

In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associated with dominance cones via the assumption of the quasiconcavity of the objectives. Necessary as well as sufficient conditions for such quasiconcave multiobjective programming problems are obtained.The author is indebted to one of the referees for detailed constructive comments and suggestions. Thanks are also due to the late Professor Abraham Charnes, University of Texas at Austin, and Professor Zhimin Huang, Adelphi University.