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The Cone-Subdifferential Stability for Perturbed Optimizations of Sed-Valued Maps in Banach Space

Hu Yuda, Shanlin Li

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Abstract

The cone-subdifferential stability for perturbed vector optimization of set-valued maps in Banach space is studied in this paper. Under condition that the objective and consraint maps are semi-continuous and cone-convex, the stability of cone-efficient point set and cone-weakly efficient point set are obtained in the context of cone-subdifferential, respectively.

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What this paper is about

The cone-subdifferential stability for perturbed vector optimization of set-valued maps in Banach space is studied in this paper. Under condition that the objective and consraint maps are semi-continuous and cone-convex, the stability of cone-efficient point set and cone-weakly efficient point set are obtained in the context of cone-subdifferential, respectively.

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Available abstract

The cone-subdifferential stability for perturbed vector optimization of set-valued maps in Banach space is studied in this paper. Under condition that the objective and consraint maps are semi-continuous and cone-convex, the stability of cone-efficient point set and cone-weakly efficient point set are obtained in the context of cone-subdifferential, respectively.

Key concepts: Subderivative, Mathematics, Cone (formal languages), Banach space, Dual cone and polar cone, Mathematical analysis, Stability (learning theory), Context (archaeology)

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