ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS

A generalized nondifierentiable fractional optimization prob- lem (GFP), which consists of a maximum objective function deflned by flnite fractional functions with difierentiable functions and support func- tions, and a constraint set deflned by difierentiable functions, is consid- ered. Recently, Kim et al. (Journal of Optimization Theory and Applica- tions 129 (2006), no. 1, 131{146) proved optimality theorems and duality theorems for a nondifierentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose com- ponents are fractional functions with difierentiable functions and support functions, and a constraint set deflned by difierentiable functions. In fact if " is a solution of (GFP), then " is a weakly e-cient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).