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Projection Methods in Conic Optimization

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Didier Henrion

    (CNRS, LAAS, Toulouse
    Czech Technical University in Prague)

  • Jérôme Malick

    (CNRS, LJK, Grenoble, INRIA)

Abstract

There exist efficient algorithms to project a point onto the intersection of a convex conic 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.

Suggested Citation

  • Didier Henrion & Jérôme Malick, 2012. "Projection Methods in Conic Optimization," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 565-600, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_20
    DOI: 10.1007/978-1-4614-0769-0_20
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    Citations

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    Cited by:

    1. Maxim Bouev & Ilia Manaev & Aleksei Minabutdinov, 2013. "Finding the Nearest Valid Covariance Matrix: An FX Market Case," EUSP Department of Economics Working Paper Series Ec-07/13, European University at St. Petersburg, Department of Economics.
    2. Goran Banjac & Paul Goulart & Bartolomeo Stellato & Stephen Boyd, 2019. "Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 490-519, November.
    3. Aleksei Minabutdinov & Ilia Manaev & Maxim Bouev, 2014. "Finding The Nearest Valid Covariance Matrix: A Fx Market Case," HSE Working papers WP BRP 32/FE/2014, National Research University Higher School of Economics.

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