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Weak \(E\)-optimal solution in vector optimization. (English) Zbl 1304.90191

Summary: In a real locally convex Hausdorff topological vector space, we first introduce the concept of nearly \(E\)-subconvexlikeness of set-valued maps via improvement set and obtain an alternative theorem. Furthermore, under the assumption of nearly subconvexlikeness, we establish scalarization theorem, Lagrange multiplier theorem, weak \(E\)-saddle point criteria and weak \(E\)-duality for weak \(E\)-optimal solution in vector optimization with set-valued maps. We also propose some examples to illustrate the main results.

MSC:

90C29 Multi-objective and goal programming
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
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