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Slopes, Error Bounds and Weak Sharp Pareto Minima of a Vector-Valued Map

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  • Xuan Duc Ha Truong

    (Vietnam Academy of Science and Technology)

Abstract

In this paper, we provide a detailed study of the upper and lower slopes of a vector-valued map recently introduced by Bednarczuk and Kruger. We show that these slopes enjoy most properties of the strong slope of a scalar-valued function and can be explicitly computed or estimated in the convex, strictly differentiable, linear cases. As applications, we obtain error bounds for lower level sets (in particular, a Hoffman-type error bound for a system of linear inequalities in the infinite-dimensional space setting, existence of weak sharp Pareto minima) and sufficient conditions for Pareto minima.

Suggested Citation

  • Xuan Duc Ha Truong, 2018. "Slopes, Error Bounds and Weak Sharp Pareto Minima of a Vector-Valued Map," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 634-649, March.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1240-6
    DOI: 10.1007/s10957-018-1240-6
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