Projection methods in conic optimization

Didier Henrion (1) , Jérôme Malick (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques.

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion, Jérôme Malick. Projection methods in conic optimization. Miguel F. Anjos and Jean B. Lasserre. Handbook on Semidefinite, Conic and Polynomial Optimization, Springer, pp.565-600, 2012, International Series in Operations Research & Management Science Volume 166, 9781461407683. ⟨10.1007/978-1-4614-0769-0_20⟩. ⟨hal-00574437⟩