Quasi-convex functions and applications to optimality conditions in nonlinear programming

摘要

We establish necessary and sufficient optimality conditions for quasi-convex programming. First, we treat some properties of the normal cone to the level set of a lower semicontinuous quasi-convex function defined on a Banach space. Next, we get our conditions via some variational inequalities. (C) 2000 Elsevier Science Ltd. All rights reserved. [References: 4]