Vector fractional programming with quasiinvexity on Riemannian manifolds
Ştefan Mititelu, Constantin Udrişte · Annual Conference on Computers · 2008
This paper establishes necessary conditions of Karush-Kuhn-Tucker type for the efficiency of an admissible solution in a vector fractional Pareto programming problem on a Riemannian manifold. In this context we develop a duality of Mond-Weir type in which the dual program has the same objective as vector fractional function. Our duality is based on direct and converse theorems for weak duality in the context of (ρ, b)-quasiinvexity with respect to the same application η. The paper is divided in four sections. Section 1 introduces some special invexities. Section 2 formulates the aims of the paper regarding a suitable vectorial programming. In Section 3 are established necessary conditions of Karush-Tucker type for the efficiency of a point in a vector fractional Pareto programming problem. Section 4 develops a duality of Mend-Weir type for the same problem, based on direct and converse weak duality theorems. This duality uses the notion of quasi (η, ρ, b)-invexity for the program functions.