Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems

Proper Efficiency for Set-Valued Optimization Problems and Vector Variational-Like Inequalities

“…Yang and Yang [24] derived some relations between a solution of a Minty VVLI and an efficient solution or a weakly efficient solution to the VOP under the assumptions of pseudoinvexity. Al-Homidan and Ansari [1] also studied the relationship between the solution to VVLIs and a efficient solution or a weakly efficient solution to nonsooth VOPs involving nondifferential invex functions. Very recently, Long et al [19] generalized the results of [1] to nondifferential pseudoinvexity.…”

“…Al-Homidan and Ansari [1] also studied the relationship between the solution to VVLIs and a efficient solution or a weakly efficient solution to nonsooth VOPs involving nondifferential invex functions. Very recently, Long et al [19] generalized the results of [1] to nondifferential pseudoinvexity. For other results on this topic, we refer readers to [2,3,4,17,20,22,23] and the references therein.…”

Generalized vector variational-like inequalities and vector optimization

“…Since then, several researchers have studied VOP by using different kinds of MVVI under different assumptions. See, for example, [1,3,5,7,9,11,[13][14][15][16]19,20] and references therein. Yang et al [19] extended the results of Giannessi [8] for differentiable but pseudoconvex functions.…”

“…In particular, they extended the results of Giannessi [8] and Yang et al [19] for differentiable but pseudoinvex vector-valued functions. Very recently, Al-Homidan and Ansari [1] and Rezaie and Zafarani [15] considered different kinds of generalized Minty vector variational-like inequality problems, generalized Stampacchia vector variational-like inequality problems and a nonsmooth vector optimization problem under nonsmooth invexity assumption. In [1], we studied the relationship among these problems under nonsmooth invexity assumption.…”

“…Very recently, Al-Homidan and Ansari [1] and Rezaie and Zafarani [15] considered different kinds of generalized Minty vector variational-like inequality problems, generalized Stampacchia vector variational-like inequality problems and a nonsmooth vector optimization problem under nonsmooth invexity assumption. In [1], we studied the relationship among these problems under nonsmooth invexity assumption. We also considered the weak formulations of a generalized Minty vector variational-like inequality problem and a generalized Stampacchia vector variational-like inequality problem and gave some relationships between the solutions of these problems and a weak efficient solution of a vector optimization problem.…”