Abstract
In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.
Highlights
Multiobjective semi-infinite programming problems (MOSIPs) arise when more than one objective function is to be optimized over the feasible region described by an infinite number of constraints
Motivated by Achtziger and Kanzow [ ], Golestani and Nobakhtian [ ] and Pandey and Mishra [ ], we extend the concept of the strong KKT optimality conditions for the MOSIPs with vanishing constraints (MOSIPVCs) that do not involve any constraint qualification
3 Strong KKT type sufficient optimality conditions We extend Definitions . and . of Hoheisel and Kanzow [ ] to the case of the multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC)
Summary
Multiobjective semi-infinite programming problems (MOSIPs) arise when more than one objective function is to be optimized over the feasible region described by an infinite number of constraints. In Section , we define stationary points and establish strong KKT type optimality for MOSIPVC. F is said to be generalized convex at xif, for each x ∈ Rn and any ξ ∈ ∂cf (x), f (x) – f (x) ≥ ξ , x – x ,
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