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Projection methods in conic optimization. (English) Zbl 1334.90105
Anjos, Miguel F. (ed.) et al., Handbook on semidefinite, conic and polynomial optimization. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). International Series in Operations Research & Management Science 166, 565-600 (2012).
Summary: 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.
For the entire collection see [Zbl 1235.90002].

MSC:
90C22 Semidefinite programming
90C90 Applications of mathematical programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
Software:
PENNON; SeDuMi; SDPT3; DIMACS
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