Lower Envelopes and Steepest Descent Directions in Vector Optimization

Details Lower Envelopes and Steepest Descent Directions in Vector Optimization Lower Envelopes and Steepest Descent Directions in Vector Optimization

2011-08-09

arxiv.org/abs/1108.1969v1

Mathematics

Functional Analysis

12 pages

Scientific paper

The purpose of the paper is to give a complete characterization of the continuity of lower envelopes in the infinite dimensional spaces in terms of the notion of c-regularity. As an application we introduce a variational unconstrained vector optimization problem for smooth functions and characterize when the variational steepest descent directions are continuous in terms of the generating sets which are considered.

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