A barrier method in convex vector optimization with generalized inequality constraints
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In this note we present a barrier method for vector optimization problems with inequality constraints. To this aim, we firstly investigate some constraint qualification conditions and we compare them to the corresponding ones in literature. Then, we define a barrier function and observe that its basic properties do work for fairly general situations, while for meaningful convergence results of the associated barrier method we should restrict ourselves to convex case and finite dimensional setting.
KeywordsOpenness Vector convexity Gerstewitz scalarization Barrier method
This work was supported by a grant of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2016-0188, within PNCDI III.