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

References

• [1] Ahmadi A, Majumdar A (2016) Some applications of polynomial optimization in operations research and real-time decision making. Optim. Lett. 10(4):709–729.Crossref, Google Scholar
• [2] Ahmadi A, Majumdar A (2019) DSOS and SDSOS optimization: More tractable alternatives to sum of squares and semidefinite optimization. SIAM J. Appl. Algebraic Geometry. Forthcoming.Google Scholar
• [3] Atamtürk A, Gómez A (2018) Strong formulations for quadratic optimization with M-matrices and indicator variables. Math. Programming 170(1):141–176.Crossref, Google Scholar
• [4] Billionnet A, Elloumi S, Lambert A (2012) Extending the QCR method to the case of general mixed integer programs. Math. Programming 131(1):381–401.Crossref, Google Scholar
• [5] Boman EG, Chen D, Parekh O, Toledo S (2005) On factor width and symmetric H-matrices. Linear Algebra Appl. 405:239–248.Crossref, Google Scholar
• [6] Ceria S, Soares J (1999) Convex programming for disjunctive convex optimization. Math. Programming 86(3):595–614.Crossref, Google Scholar
• [7] Cui XT, Zheng XJ, Zhu SS, Sun XL (2013) Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems. J. Global Optim. 56(4):1409–1423.Crossref, Google Scholar
• [8] Frangioni A, Gentile C (2006) Perspective cuts for a class of convex 0–1 mixed integer programs. Math. Programming 106(2):225–236.Crossref, Google Scholar
• [9] Frangioni A, Gentile C (2007) SDP diagonalizations and perspective cuts for a class of nonseparable MIQP. Oper. Res. Lett. 35(2):181–185.Crossref, Google Scholar
• [10] Frangioni A, Gentile C (2009) A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes. Oper. Res. Lett. 37(3):206–210.Crossref, Google Scholar
• [11] Frangioni A, Furini F, Gentile C (2016) Approximated perspective relaxations: A project and lift approach. Comput. Optim. Appl. 63(3):705–735.Crossref, Google Scholar
• [12] Frangioni A, Furini F, Gentile C (2017) Improving the approximated projected perspective reformulation by dual information. Oper. Res. Lett. 45(5):519–524.Crossref, Google Scholar
• [13] Frobenius FG (1912) Über Matrizen aus nicht negativen Elementen (De Gruyter, Berlin).Google Scholar
• [14] Jeon H, Linderoth J, Miller A (2014) Quadratic cone cutting surfaces for quadratic programs with onoff constraints. Discrete Optim. 24:32–50.Crossref, Google Scholar
• [15] Majumdar A, Ahmadi A, Tedrake R (2014) Control and verification of high-dimensional systems with DSOS and SDOS programming. Proc. 53rd IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 394–401.Crossref, Google Scholar
• [16] Perron O (1907) Zur theorie der matrices. Mathematische Annalen 64:248–263.Crossref, Google Scholar
• [17] Plemmons R (1977) M-matrix characterizations. I - Nonsingular M-matrices. Linear Algebra Appl. 18(2):175–188.Crossref, Google Scholar
• [18] Rockafellar R (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [19] Ruozzi N, Tatikonda S (2013) Message-passing algorithms for quadratic minimization. J. Machine Learn. 14:2287–2314.Google Scholar
• [20] Sherali H, Adams W (2009) A reformulation-linearization technique (RLT) for semi-infinite and convex programs under mixed 0-1 and general discrete restrictions. Discrete Appl. Math. 157(6):1319–1333.Crossref, Google Scholar
• [21] Zheng X, Sun X, Li D (2014) Improving the performance of MIQP solvers for quadratic programs with cardinality and minimum threshold constraints: A semidefinite program approach. INFORMS J. Comput. 26(4):690–703.Link, Google Scholar