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Projection methods in conic optimization

Didier Henrion(henrion***at***laas.fr)
Jerome Malick(jerome.malick***at***inria.fr)

Abstract: 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.

Keywords: conic optimization; convex optimization; projection

Category 1: Convex and Nonsmooth Optimization

Category 2: Linear, Cone and Semidefinite Programming

Category 3: Optimization Software and Modeling Systems

Citation: To appear as a contributed chapter of "Handbook of Semidefinite, Cone and Polynomial Optimization" edited by M. Anjos and J. B. Lasserre, Springer, 2011.

Download: [PDF]

Entry Submitted: 03/08/2011
Entry Accepted: 03/08/2011
Entry Last Modified: 03/08/2011

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