Lower Envelopes and Steepest Descent Directions in Vector Optimization
  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. 
Nihat Gokhan Gogus
math.FA math.OC