Regularity conditions for constrained extremum problems via image space approach: the linear case

Abstract

In the theory of constrained extremum problems, optimality conditions can be formulated in several different ways: among the most used are those of Lagrangian type. In the paper we want to revisit again the problem of establishing regularity assumptions (or constraint qualifications, the difference in the terminology whether consisting in the condition involves or not the objective function) for a Lagrangian type optimality condition. We will develop the study via a recently proposed approach [3]: the image space analysis. This approach has showed many interesting developments in many topics of optimization theory (optimality conditions, penalty methods, duality theory etc). We show that, also in this field, it represents a powerful tool for developing the analysis.

Research partially developed during the stay of the first author at the University of Pisa with a fellowship from the C.N.R. of Italy.