$$\varepsilon $$-Quasi-Weakly Solution for Semi-infinite Vector Optimization Problems with Data Uncertainty

On approximate positively properly efficient solutions in nonsmooth semi-infinite multiobjective optimization problems with data uncertainty

“…Motivated by the definition of generalized convexity due to [42], we introduce the concepts as follows: Definition 4.2. We say that (p − s q, g T ) is generalized convex on Ω at x ∈ Ω if, for any…”

“…Motivated by the definition of generalized convexity due to [42], we introduce the concept as follows.…”

“…Optimality conditions and duality theorems for approximate solutions of a multiobjective optimization problems were studied in [29,30,31] and optimality conditions/duality theorems/saddle point theorems for approximate solutions of optimization problems with infinite constraints were given in [32,33,34,35,36,37,38,39]. On the other hand, optimality conditions/duality theorems for approximate solutions of robust optimization problems with infinite constraints were obtained in [40,41,42]. However, to the best of our knowledge, up to now, there is no paper devoted to ε-quasi positively properly efficient solutions of semi-infinite multiobjective optimization problems with data uncertainty.…”