Decompositions of Semidefinite Matrices and the Perspective Reformulation of Nonseparable Quadratic Programs

We study the problem of decomposing the Hessian matrix of a mixed integer convex quadratic program (MICQP) into the sum of positive semidefinite 2 × 2 matrices. Solving this problem enables the use...

[1]  O. Perron Zur Theorie der Matrices , 1907 .

[2]  丸山 徹 Convex Analysisの二,三の進展について , 1977 .

[3]  R. Plemmons M-matrix characterizations.I—nonsingular M-matrices , 1977 .

[4]  Sebastián Ceria,et al.  Convex programming for disjunctive convex optimization , 1999, Math. Program..

[5]  Ojas D. Parekh,et al.  On Factor Width and Symmetric H-matrices , 2005 .

[6]  Claudio Gentile,et al.  Perspective cuts for a class of convex 0–1 mixed integer programs , 2006, Math. Program..

[7]  Claudio Gentile,et al.  SDP diagonalizations and perspective cuts for a class of nonseparable MIQP , 2007, Oper. Res. Lett..

[8]  Claudio Gentile,et al.  A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes , 2009, Oper. Res. Lett..

[9]  Hanif D. Sherali,et al.  A Reformulation-Linearization Technique (RLT) for semi-infinite and convex programs under mixed 0-1 and general discrete restrictions , 2009, Discret. Appl. Math..

[10]  A. Billionnet,et al.  Extending the QCR method to the case of general mixed integer programs , 2012 .

[11]  Alain Billionnet,et al.  Extending the QCR method to general mixed-integer programs , 2010, Mathematical Programming.

[12]  S. S. Zhu,et al.  Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems , 2012, Journal of Global Optimization.

[13]  Sekhar Tatikonda,et al.  Message-passing algorithms for quadratic minimization , 2012, J. Mach. Learn. Res..

[14]  Amir Ali Ahmadi,et al.  Control and verification of high-dimensional systems with DSOS and SDSOS programming , 2014, 53rd IEEE Conference on Decision and Control.

[15]  Duan Li,et al.  Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach , 2014, INFORMS J. Comput..

[16]  C. Gentile,et al.  Approximated Perspective Relaxations : a Project & Lift Approach , 2015 .

[17]  Claudio Gentile,et al.  Approximated perspective relaxations: a project and lift approach , 2016, Comput. Optim. Appl..

[18]  Amir Ali Ahmadi,et al.  Some applications of polynomial optimization in operations research and real-time decision making , 2015, Optimization Letters.

[19]  Jeff T. Linderoth,et al.  Quadratic cone cutting surfaces for quadratic programs with on-off constraints , 2017, Discret. Optim..

[20]  Claudio Gentile,et al.  Improving the Approximated Projected Perspective Reformulation by dual information , 2017, Oper. Res. Lett..

[21]  Alper Atamtürk,et al.  Strong formulations for quadratic optimization with M-matrices and indicator variables , 2018, Math. Program..

[22]  Alper Atamtürk STRONG FORMULATIONS FOR QUADRATIC OPTIMIZATION WITH M-MATRICES AND SEMI-CONTINUOUS VARIABLES , 2018 .

[23]  Amir Ali Ahmadi,et al.  DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization , 2017, SIAM J. Appl. Algebra Geom..