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Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used.
Convex Analysis
Ralph Tyrrell Rockafellar · 1970
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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 1985
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Cliques, colorings and satisfiability. 2nd DIMACS implementation challenge, 1993
David J. Johnson and Michael A. Trick · 1996
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Variational Analysis
Ralph Tyrrell Rockafellar and J-B. Roger Wets · 1998
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On copositive programming and standard quadratic optimization problems
Immanuel M. Bomze, Mirjam Dür, Etienne de Klerk, Cornelis Roos, Arie J. Quist, and Tamás Terlaky · 2000
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Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
Pablo A. Parrilo · 2000
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Solving standard quadratic optimization problems via linear, semidefinite and copositive programming
Immanuel M. Bomze and Etienne de Klerk · 2002
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Approximation of the stability number of a graph via copositive programming
Etienne de Klerk and Dmitrii V. Pasechnik · 2002
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Applications of second-order cone programming
Miguel Sousa Lobo, Lieven Vandenberghe, Stephen Boyd, and Hervé Lebret · 2002
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Completely positive matrices
Berman Abraham and Shaked-monderer Naomi · 2003
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On factor width and symmetric h-matrices
Erik G. Boman, Doron Chen, Ojas Parekh, and Sivan Toledo · 2005
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Challenge problems: Independent sets in graphs
Neil Sloane · 2005
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Computing the stability number of a graph via linear and semidefinite programming
Javier Pena, Juan Vera, and Luis F. Zuluaga · 2007
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An adaptive linear approximation algorithm for copositive programs
Stefan Bundfuss and Mirjam Dür · 2009
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On the copositive representation of binary and continuous nonconvex quadratic programs
Samuel Burer · 2009
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On the accuracy of uniform polyhedral approximations of the copositive cone
E. Alper Yıldırım · 2012
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CVX: Matlab software for disciplined convex programming, version 2.1
Michael Grant and Stephen Boyd · 2014
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New approximations for the cone of copositive matrices and its dual
Jean B. Lasserre · 2014
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Optimization over structured subsets of positive semidefinite matrices via column generation
Amir Ali Ahmadi, Sanjeeb Dash, and Georgina Hall · 2017
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Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming
Amir Ali Ahmadi and Georgina Hall · 2017
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Inner approximations of completely positive reformulations of mixed binary quadratic programs: a unified analysis
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Copositive programming – a survey
Mirjam Dür · 2010
Cited alongside, same era.
Think co(mpletely) positive! Matrix properties, examples and a clustered bibliography on copositive optimization
Immanuel M. Bomze, Werner Schachinger, and Gabriele Uchida · 2012
Cited alongside, same era.
Copositive programming
Samuel Burer · 2012
Cited alongside, same era.
E. Alper Yıldırım · 2017
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Partial facial reduction: simplified, equivalent sdps via approximations of the psd cone
Frank Permenter and Pablo Parrilo · 2018
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Dsos and sdsos optimization: more tractable alternatives to sum of squares and semidefinite optimization
Amir Ali Ahmadi and Anirudha Majumdar · 2019
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