On Minty variational principle for nonsmooth vector optimization problems with generalized approximate convexity

Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity

“…We have established the relationships between this problem and vector variational inequality problems under the hypotheses of e-approximate LU-convexity or generalized e-approximate LU-convexity. Hence, our presented results extend and improve the corresponding main results obtained in [17,18,20].…”

“…i) We can show that similar results of this section can be obtained when using e-approximate LU-convexity assumptions. ii) As the interval-valued vector optimization problems is more general than vector optimization problems, the results of this section represent a generalization of some results obtained in [17,18].…”

“…3. There is no relation between approximate pseudo e-convex functions of type II and approximate quasi e-convex functions of type II and approximate e-convex functions (see [18]).…”

“…On the other hand, a considerable and growing interest has been centered about studying the relationship between vector optimization problems and vector variational inequalities. In particular, many results providing optimality conditions in terms of vector variational inequalities were proven for vector-valued objective functions; see for instance [8][9][10][11] for the smooth case, [12][13][14] for the nonsmooth case and [15][16][17][18][19] for some more recent results. With respect to interval-valued objective functions, Zhang et al [6,20] studied optimality conditions under the assumption of LU-convexity introduced by Wu [4] as an extension of convexity for real-valued functions.…”

Interval-valued vector optimization problems involving generalized approximate convexity

“…3. There is no relation between approximate pseudo e-convex functions of type II and approximate quasi e-convex functions of type II and approximate e-convex functions (see [6]).…”