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Vector variational-like inequalities with generalized bifunctions defined on nonconvex sets. (English) Zbl 1182.47046
In this paper, the nonemptiness and compactness of solution sets for Stampacchia vector variational-like inequalities (for short, SVVLIs) and Minty vector variational-like inequalities (for short, MVVLIs) with generalized bifunctions defined on nonconvex sets are investigated by introducing the concepts of generalized weak cone-pseudomonotonicity and generalized (proper) cone-suboddness. The equivalent relations between a solution of SVVLIs and MVVLIs, and a generalized weakly efficient solution of vector optimization problems are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of the Clarke generalized directional derivative.

MSC:
47J20 Variational and other types of inequalities involving nonlinear operators (general)
90C29 Multi-objective and goal programming
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