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Borwein–Preiss Vector Variational Principle

Alexander Y. Kruger (a.kruger***at***federation.edu.au)
Somyot Plubtieng (somyotp***at***nu.ac.th)
Thidaporn Seangwattana (seangwattana_t***at***hotmail.com)

Abstract: This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein–Preiss variational principle due to Li and Shi, J. Math. Anal. Appl. 246(1), 308–319 (2000). We introduce and characterize two seemingly new natural concepts of epsilon-minimality, one of them dependent on the chosen element in the ordering cone and the fixed “gauge-type” function.

Keywords: Borwein-Preiss variational principle, smooth variational principle, gauge-type function, perturbation

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 08/31/2015
Entry Accepted: 08/31/2015
Entry Last Modified: 08/31/2015

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