Advertisement

A Convex Optimization Toolbox

  • J. Frédéric BonnansEmail author
Chapter
Part of the Universitext book series (UTX)

Abstract

This chapter presents the duality theory for optimization problems, by both the minimax and perturbation approach, in a Banach space setting. Under some stability (qualification) hypotheses, it is shown that the dual problem has a nonempty and bounded set of solutions. This leads to the subdifferential calculus, which appears to be nothing but a partial subdifferential rule. Applications are provided to the infimal convolution, as well as recession and perspective functions. The relaxation of some nonconvex problems is analyzed thanks to the Shapley–Folkman theorem.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Inria-Saclay and Centre de Mathématiques AppliquéesÉcole PolytechniquePalaiseauFrance

Personalised recommendations