Saddle points and Lagrangian-type duality for discrete minmax fractional subset programming problems with generalized convex functions

In this paper we present four sets of saddle-point-type optimality conditions, construct two Lagrangian-type dual problems, and prove weak and strong duality theorems for a discrete minmax fractional subset programming problem.We establish these optimality and duality results under appropriate (b,φ,ρ, θ)-convexity hypotheses.  2005 Elsevier Inc. All rights reserved.