On the degeneracy phenomenon in optimization problems with inequality constraints

Abstract

In this paper, we discuss the degeneracy phenomenon in optimization problems with inequality constraints. We start by describing this phenomenon in the context of mathematical programming problems, recalling the Fritz-John and Kuhn-Tucker conditions. Later, we address the degeneracy phenomenon in the context of optimal control problems. We review and discuss nondegenerate Necessary Conditions of Optimality for optimal control problems with state constraints. An overview of the main literature in this area is made, including a comparison with some recent results from the authors.