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Characterizations of nonemptiness and compactness of the set of weakly efficient solutions for convex vector optimization and applications. (English) Zbl 1018.90048

Summary: We give characterizations for the nonemptiness and compactness of the set of weakly efficient solutions of an unconstrained/constrained convex vector optimization problem with extended vector-valued functions in terms of the 0-coercivity of some scalar functions. Finally, we apply these results to discuss solution characterizations of a constrained convex vector optimization problem in terms of solutions of a sequence of unconstrained vector optimization problems which are constructed with a general nonlinear Lagrangian.

MSC:

90C29 Multi-objective and goal programming
90C31 Sensitivity, stability, parametric optimization
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