DUALITY FOR NONLINEAR FRACTIONAL PROGRAMMING INVOLVING GENERALIZED ρ-SEMILOCALLY b-PREINVEX FUNCTIONS

We consider a nonlinear fractional programming problem with inequality constraints, where the functions involved are ρ-semilocally b-preinvex, ρ-semilocally explicitly b-preinvex, ρ-semilocally quasi b-preinvex, ρ-semilocally pseudo bpreinvex and ρ-semi-locally strongly pseudo b-preinvex functions. Necessary optimality conditions are obtained in terms of the right derivative of a function along one direction. Wolfe and Mond-Weir type duals are associated, and weak, direct and strict converse duality are established. Our results generalize those obtained by Lyall, Suneja and Aggarwal [7], Patel [9], Stancu-Minasian [14], [16] and Stancu-Minasian and Andreea Mădălina Stancu [17], [18].