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( $$\epsilon $$ ϵ -)Efficiency in difference vector optimization

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  • Mounir El Maghri

Abstract

The paper deals with the problem of characterizing Pareto optima (efficient solutions) for the difference of two mappings vector-valued in a finite or infinite-dimensional preordered space. Closely related to the well-known optimality criterion of scalar DC optimization, a mixed vectorial condition is obtained in terms of both strong (Fenchel) and weak (Pareto) $$\epsilon $$ ϵ -subdifferentials that completely characterizes the exact or approximate weak efficiency. This condition also allows to deal with some special restricted mappings. Moreover, the condition established in the literature in terms of strong $$\epsilon $$ ϵ -subdifferentials for characterizing the strongly efficient solutions (usual optima), is shown here to remain valid without assuming that the objective space is order-complete. Copyright Springer Science+Business Media New York 2015

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  • Mounir El Maghri, 2015. "( $$\epsilon $$ ϵ -)Efficiency in difference vector optimization," Journal of Global Optimization, Springer, vol. 61(4), pages 803-812, April.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:4:p:803-812
    DOI: 10.1007/s10898-014-0204-0
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. S. Bolintinéanu & M. El Maghri, 1998. "Second-Order Efficiency Conditions and Sensitivity of Efficient Points," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 569-592, September.
    3. F. Flores-BAZÁN & W. Oettli, 2001. "Simplified Optimality Conditions for Minimizing the Difference of Vector-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 571-586, March.
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