Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions

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

“…Furthermore, a general dual was formulated and duality results were proved using concepts of generalized semilocally preinvex functions. Thus, results of Preda [28], Preda and Stancu-Minasian [29], and Preda et al [30] were generalized. Mishra et al [5] extended the issues of Preda [7] to the case of semilocally type I and related functions, generalizing results of Preda [7] and Stancu-Minasian [31].…”

“…Thus, results of Preda [28], Preda and Stancu-Minasian [29], and Preda et al [30] were generalized. Mishra et al [5] extended the issues of Preda [7] to the case of semilocally type I and related functions, generalizing results of Preda [7] and Stancu-Minasian [31]. Niculescu [6] extended the work of Mishra et al [5] by using concepts of generalized -semilocally type I-preinvex functions.…”

“…The field of multiobjective fractional optimization has been naturally enriched by the introductions and applications of various types of convexity theory, with and without differentiability assumptions, and in the framework of symmetric duality, variational problems, minimax programming, continuous time programming, and so forth. More specifically, works in the area of nonsmooth setting can be found in Chen [1], Kim et al [2], Kuk et al [3], Mishra and Rautela [4], Mishra et al [5], Niculescu [6], Preda [7], and Soleimani-damaneh [8]. Efficiency conditions and duality models for multiobjective fractional subset programming problems are studied by Preda et al [9], Verma [10], and Zalmai [11][12][13].…”

“…The concept of semilocally convex functions was introduced by Ewing [25] and was further extended to semilocally quasiconvex, semilocally pseudoconvex functions by Kaul and Kaur [26,27]. Other generalizations of semilocally convex functions and their properties were investigated in 2 International Journal of Mathematics and Mathematical Sciences Mishra and Rautela [4], Mishra et al [5], Niculescu [6], Preda [7,28], Preda and Stancu-Minasian [29], Preda et al [30], and Stancu-Minasian [31].…”

“…In Preda [7], necessary and sufficient efficiency conditions for a nonlinear fractional multiple objective programming problem are obtained involving -semidifferentiable functions. Furthermore, a general dual was formulated and duality results were proved using concepts of generalized semilocally preinvex functions.…”