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

Xuan Duc Ha Truong ()
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Xuan Duc Ha Truong: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 3, No 7, 634-649

Abstract: 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.

Keywords: Vector-valued map; Slope; Error bound; Weak sharp Pareto minima; 49J53; 58C06; 90C29 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1240-6

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