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Stability of Multiobjective Programming under the Constraint Cone and the Control Cone Perturbations

Xuan Zhou

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Abstract

The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis,the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective projiamming problem under two perturbations are obtained in Banach space.

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What this paper is about

The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis,the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective projiamming problem under two perturbations are obtained in Banach space.

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Available abstract

The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis,the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective projiamming problem under two perturbations are obtained in Banach space.

Key concepts: Cone (formal languages), Banach space, Dual cone and polar cone, Mathematics, Perturbation (astronomy), Second-order cone programming, Constraint (computer-aided design), Mathematical analysis

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