Optimality conditions and duality in multiple objective programming involving semilocally convex and related functions

On nonlinear multiple objective fractional programming involving semilocally type-I univex functions

“…Definition 2.1 [12] We say that the set X 0 ⊆ R n is η-locally starshaped set at x,x ∈ X 0 if for any x ∈ X 0 , there exists 0 < a η (x,x) 1 such thatx + λη(x,x) ∈ X 0 for any λ ∈ [0, a η (x,x)]. Definition 2.2 [12] Let f : X 0 → R n be a function, where X 0 ⊆ R n is η-locally starshaped set at x ∈ X 0 .…”

“…Definition 2.2 [12] Let f : X 0 → R n be a function, where X 0 ⊆ R n is η-locally starshaped set at x ∈ X 0 . We say that f is:…”

“…Ewing [3] introduced semilocally convex functions which he applied it to derive sufficient optimality conditions for variational and control problems. Some generalizations of semilocally convex functions and their properties were investigated in Kaul and Kaur [6,7], Preda [12,13], Preda and Stancu-Minasian [14,15] and Stancu-Minasian [17] obtained optimality and duality results for nonlinear programming problems involving semilocally preinvex and related functions. Stancu [16] studied optimality and duality in nonlinear programming involving ρ-semilocally b-preinvex functions.…”

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

“…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].…”

“…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].…”