Borwein–Preiss vector variational principle

Positivity - Tập 21 - Trang 1273-1292 - 2017
A. Y. Kruger1, S. Plubtieng2, T. Seangwattana2
1Centre for Informatics and Applied Optimization, Faculty of Science and Technology, Federation University Australia, Ballarat, Australia
2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand

Tóm tắt

This article extends to the vector setting the results of our previous work Kruger et al. (J Math Anal Appl 435(2):1183–1193, 2016) 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. doi: 10.1006/jmaa.2000.6813 ). We introduce and characterize two seemingly new natural concepts of $$\varepsilon $$ -minimality, one of them dependent on the chosen element in the ordering cone and the fixed “gauge-type” function.

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