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Approximate Efficiency and Scalar Stationarity in Unbounded Nonsmooth Convex Vector Optimization Problems

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  • S. BOLINTINÉANU

    (Université de Perpignan)

Abstract

We deal with extended-valued nonsmooth convex vector optimization problems in infinite-dimensional spaces where the solution set (the weakly efficient set) may be empty. We characterize the class of convex vector functions having the property that every scalarly stationary sequence is a weakly-efficient sequence. We generalize the results obained in the scalar case by Auslender and Crouzeix about asymptotically well-behaved convex functions and improve substantially the few results known in the vector case.

Suggested Citation

  • S. Bolintinéanu, 2000. "Approximate Efficiency and Scalar Stationarity in Unbounded Nonsmooth Convex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 265-296, August.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:2:d:10.1023_a:1004695229456
    DOI: 10.1023/A:1004695229456
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    Cited by:

    1. Ceng, Lu-Chuan & Yao, Jen-Chih, 2007. "Approximate proximal methods in vector optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 1-19, November.
    2. L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.

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