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Handbook on semidefinite, conic and polynomial optimization. (English) Zbl 1235.90002
International Series in Operations Research & Management Science 166. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). xi, 960 p. (2012).

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The articles of mathematical interest will be reviewed individually.
Indexed articles:
Anjos, Miguel F.; Lasserre, Jean B., Introduction to semidefinite, conic and polynomial optimization, 1-22 [Zbl 1334.90095]
Laurent, Monique; Rostalski, Philipp, The approach of moments for polynomial equations, 25-60 [Zbl 1334.90111]
Ranestad, Kristian, Algebraic degree in semidefinite and polynomial optimization, 61-75 [Zbl 1334.90114]
Helton, J. William; Nie, Jiawang, Semidefinite representation of convex sets and convex hulls, 77-112 [Zbl 1334.90104]
Gouveia, João; Thomas, Rekha, Convex hulls of algebraic sets, 113-138 [Zbl 1334.90102]
Chlamtac, Eden; Tulsiani, Madhur, Convex relaxations and integrality gaps, 139-169 [Zbl 1334.90099]
De Klerk, Etienne; Filho, Fernando M. De Oliveira; Pasechnik, Dmitrii V., Relaxations of combinatorial problems via association schemes, 171-199 [Zbl 1334.90100]
Burer, Samuel, Copositive programming, 201-218 [Zbl 1334.90098]
Bachoc, Christine; Gijswijt, Dion C.; Schrijver, Alexander; Vallentin, Frank, Invariant semidefinite programs, 219-269 [Zbl 1334.90097]
Lasserre, Jean B., A “joint+marginal” approach in optimization, 271-295 [Zbl 1334.90110]
Alizadeh, F., An introduction to formally real Jordan algebras and their applications in optimization, 297-337 [Zbl 1334.90123]
Yoshise, Akiko, Complementarity problems over symmetric cones: A survey of recent developments in several aspects, 339-375 [Zbl 1334.90180]
Helton, J. William; Klep, Igor; Mccullough, Scott, Convexity and semidefinite programming in dimension-free matrix unknowns, 377-405 [Zbl 1334.90103]
Lasserre, Jean B.; Putinar, Mihai, Positivity and optimization: beyond polynomials, 407-434 [Zbl 1334.65103]
Salahi, Maziar; Terlaky, Tamás, Self-regular interior-point methods for semidefinite optimization, 437-454 [Zbl 1334.90115]
Jarre, Florian, Elementary optimality conditions for nonlinear SDPs, 455-470 [Zbl 1334.90106]
Engau, Alexander, Recent progress in interior-point methods: cutting-plane algorithms and warm starts, 471-498 [Zbl 1334.90101]
Kim, Sunyoung; Kojima, Masakazu, Exploiting sparsity in SDP relaxation of polynomial optimization problems, 499-531 [Zbl 1334.90107]
Wen, Zaiwen; Goldfarb, Donald; Scheinberg, Katya, Block coordinate descent methods for semidefinite programming, 533-564 [Zbl 1334.90118]
Henrion, Didier; Malick, Jérôme, Projection methods in conic optimization, 565-600 [Zbl 1334.90105]
Navascués, Miguel; Pironio, Stefano; Acín, Antonio, SDP relaxations for non-commutative polynomial optimization, 601-634 [Zbl 1334.90113]
van Hoeve, Willem-Jan, Semidefinite programming and constraint programming, 635-668 [Zbl 1334.90121]
Mittelmann, Hans D., The state-of-the-art in conic optimization software, 671-686 [Zbl 1334.90112]
Yamashita, Makoto; Fujisawa, Katsuki; Fukuda, Mituhiro; Kobayashi, Kazuhiro; Nakata, Kazuhide; Nakata, Maho, Latest developments in the SDPA family for solving large-scale SDPs, 687-713 [Zbl 1334.90119]
Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H., On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0, 715-754 [Zbl 1334.90117]
Kočvara, Michal; Stingl, Michael, PENNON: software for linear and nonlinear matrix inequalities, 755-791 [Zbl 1334.90108]
Sotirov, Renata, SDP relaxations for some combinatorial optimization problems, 795-819 [Zbl 1334.90116]
Palagi, Laura; Piccialli, Veronica; Rendl, Franz; Rinaldi, Giovanni; Wiegele, Angelika, Computational approaches to MAX-cut, 821-847 [Zbl 1334.90149]
Anjos, Miguel F.; Liers, Frauke, Global approaches for facility layout and VLSI floorplanning, 849-877 [Zbl 1334.90096]
Krislock, Nathan; Wolkowicz, Henry, Euclidean distance matrices and applications, 879-914 [Zbl 1334.90109]
Zhang, Youwei; d’Aspremont, Alexandre; El Ghaoui, Laurent, Sparse PCA: convex relaxations, algorithms and applications, 915-940 [Zbl 1334.90120]

MSC:
90-06 Proceedings, conferences, collections, etc. pertaining to operations research and mathematical programming
90-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operations research and mathematical programming
90C22 Semidefinite programming
90C30 Nonlinear programming
90C90 Applications of mathematical programming
00B15 Collections of articles of miscellaneous specific interest
Software:
Matlab; SDPT3
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