Lower Envelopes and Steepest Descent Directions in Vector Optimization
arXiv:1108.1969
Abstract
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.
12 pages