Mining for diamonds - Matrix generation algorithms for binary quadratically constrained quadratic problems

[1]  Franz Rendl,et al.  Conic optimization: A survey with special focus on copositive optimization and binary quadratic problems , 2021, EURO J. Comput. Optim..

[2]  Ting Kei Pong,et al.  Inner approximating the completely positive cone via the cone of scaled diagonally dominant matrices , 2018, J. Glob. Optim..

[3]  Andrea Lodi,et al.  QPLIB: a library of quadratic programming instances , 2018, Mathematical Programming Computation.

[4]  Daniel Bienstock,et al.  LP Formulations for Polynomial Optimization Problems , 2018, SIAM J. Optim..

[5]  E. Alper Yildirim.  Inner approximations of completely positive reformulations of mixed binary quadratic programs: a unified analysis , 2017, Optim. Methods Softw..

[6]  Amir Ali Ahmadi,et al.  Optimization over structured subsets of positive semidefinite matrices via column generation , 2015, Discret. Optim..

[7]  J. Malick,et al.  BiqCrunch , 2017, ACM Trans. Math. Softw..

[8]  Alberto Ceselli,et al.  Automatic Dantzig–Wolfe reformulation of mixed integer programs , 2014, Mathematical Programming.

[9]  Adam N. Letchford,et al.  Non-convex mixed-integer nonlinear programming: A survey , 2012 .

[10]  Michel Minoux,et al.  On the Solution of a Graph Partitioning Problem under Capacity Constraints , 2012, ISCO.

[11]  Immanuel M. Bomze,et al.  Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization , 2012, J. Glob. Optim..

[12]  Immanuel M. Bomze,et al.  Copositive optimization - Recent developments and applications , 2012, Eur. J. Oper. Res..

[13]  J. Lasserre,et al.  Handbook on Semidefinite, Conic and Polynomial Optimization , 2012 .

[14]  G. Nemhauser.  Column Generation for Linear and Integer Programming , 2012 .

[15]  P. Toint,et al.  A Quadratic Programming Bibliography , 2012 .

[16]  Peter J. C. Dickinson.  Geometry of the copositive and completely positive cones , 2011 .

[17]  Franz Rendl,et al.  Quadratic factorization heuristics for copositive programming , 2011, Math. Program. Comput..

[18]  Samuel Burer,et al.  Optimizing a polyhedral-semidefinite relaxation of completely positive programs , 2010, Math. Program. Comput..

[19]  Mirjam Dür,et al.  Copositive Programming – a Survey , 2010 .

[20]  M. Lübbecke.  Column Generation , 2010 .

[21]  Peter J. C. Dickinson.  AN IMPROVED CHARACTERISATION OF THE INTERIOR OF THE COMPLETELY POSITIVE CONE , 2010 .

[22]  Franz Rendl,et al.  Semidefinite Relaxations for Integer Programming , 2010, 50 Years of Integer Programming.

[23]  Adam N. Letchford,et al.  On Nonconvex Quadratic Programming with Box Constraints , 2009, SIAM J. Optim..

[24]  Samuel Burer,et al.  On the copositive representation of binary and continuous nonconvex quadratic programs , 2009, Math. Program..

[25]  Mirjam Dür,et al.  An Adaptive Linear Approximation Algorithm for Copositive Programs , 2009, SIAM J. Optim..

[26]  Stanislav Busygin,et al.  Copositive Programming , 2009, Encyclopedia of Optimization.

[27]  Mirjam Dür,et al.  Interior points of the completely positive cone. , 2008 .

[28]  Jean B. Lasserre,et al.  Convergent SDP-Relaxations in Polynomial Optimization with Sparsity , 2006, SIAM J. Optim..

[29]  Frédéric Roupin,et al.  From Linear to Semidefinite Programming: An Algorithm to Obtain Semidefinite Relaxations for Bivalent Quadratic Problems , 2004, J. Comb. Optim..

[30]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..

[31]  Etienne de Klerk,et al.  Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming , 2002, J. Glob. Optim..

[32]  Franz Rendl,et al.  Semidefinite programming and integer programming , 2002 .

[33]  Christoph Helmberg,et al.  Semidefinite programming , 2002, Eur. J. Oper. Res..

[34]  Kazuo Murota,et al.  Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework , 2000, SIAM J. Optim..

[35]  Etienne de Klerk,et al.  On Copositive Programming and Standard Quadratic Optimization Problems , 2000, J. Glob. Optim..

[36]  François Vanderbeck,et al.  On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm , 2000, Oper. Res..

[37]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[38]  B. Borchers.  CSDP, A C library for semidefinite programming , 1999 .

[39]  Charles R. Johnson,et al.  The completely positive and doubly nonnegative completion problems , 1998 .

[40]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[41]  安藤 毅.  Completely positive matrices , 1991 .

[42]  Manfred W. Padberg,et al.  The boolean quadric polytope: Some characteristics, facets and relatives , 1989, Math. Program..

[43]  Ali Ridha Mahjoub,et al.  On the cut polytope , 1986, Math. Program..

[44]  Charles R. Johnson,et al.  Positive definite completions of partial Hermitian matrices , 1984 .

[45]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[46]  M. Hall,et al.  Copositive and completely positive quadratic forms , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[47]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .