Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

Abstract

We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003)

Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints

“…This requirement is considered and viewed as a major restriction in applications. By considering the invexity with respect to different ðg i Þ i (each function involved in the studied problem is considered with respect to its own function g i instead of the same function g), Slimani and Radjef (2009, 2010a, b, 2011, 2015 and Slimani and Mishra (2014) have obtained necessary and sufficient optimality conditions and duality results for nonlinear scalar and (nondifferentiable) multiobjective problems. Ahmad (2011) has considered a nondifferentiable multiobjective problem and by using generalized univexity with respect to different ðg i Þ i , he has obtained optimality conditions and duality results.…”