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The vector-valued variational principle in Banach spaces ordered by cones with nonempty interiors. (English) Zbl 1144.58012

Summary: We prove sharpness of efficient solutions \(x_k\) to vector optimization problems resulting from Ekeland vector variational principles. We achieve this by sharpening some of the existing vector variational principles and showing that \(x_k\) remains efficient not only for perturbations in the direction \(k\) but also for other directions of perturbations.

MSC:

58E30 Variational principles in infinite-dimensional spaces
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
65K10 Numerical optimization and variational techniques
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