On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming
Published Online:2 Feb 2011https://doi.org/10.1287/moor.1100.0473
References
- , Wolkowicz H., Saigal R., Vandenberghe L. Matrix completion problems. Handbook of Semidefinite Programming: Theory, Algorithms, and Applications (2000) 27(Kluwer Academic Publishers, Boston) 533–545International Series in Operations Research and Management ScienceCrossref, Google Scholar
- Euclidean distance matrices, semidefinite programming, and sensor network localization. Portugal Math. (2010) . ForthcomingGoogle Scholar
- Recent directions in netlist partitioning: A survey. Integrated VLSI J. (1995) 19(1–2):1–81Crossref, Google Scholar
- On Lagrangian relaxation of quadratic matrix constraints. SIAM J. Matrix Anal. Appl. (2000) 22(1):41–55Crossref, Google Scholar
- Strong duality for a trust-region type relaxation of the quadratic assignment problem. Linear Algebra Appl. (1999) 301(1–3):121–136Crossref, Google Scholar
- Quadratic matrix programming. SIAM J. Optim. (2006) 17(4):1224–1238Crossref, Google Scholar
- Generalized Inverses: Theory and Applications (1974) (Wiley-Interscience, New York) Google Scholar
- Lectures on Modern Convex Optimization (2001) (Society for Industrial and Applied Mathematics (SIAM), Philadelphia) MPS/SIAM Series on OptimizationCrossref, Google Scholar
- Robust Optimization (2009) (Princeton University Press, Princeton, NJ) Princeton Series in Applied MathematicsCrossref, Google Scholar
- Semidefinite programming for ad hoc wireless sensor network localization. Proc. Third Internat. Sympos. Inform. Processing in Sensor Networks (2004) Berkeley, CA:46–54Crossref, Google Scholar
- SpaseLoc: An adaptive subproblem algorithm for scalable wireless sensor network localization. SIAM J. Optim. (2006) 17(4):1102–1128Crossref, Google Scholar
- Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem. Math. Programming (2010) 122(2, Ser. A):225–246Crossref, Google Scholar
- A low-dimensional semidefinite relaxation for the quadratic assignment problem. Math. Oper. Res. (2009) 34(4):1008–1022Link, Google Scholar
- Lower bounds for the partitioning of graphs. IBM J. Res. Development (1973) 17(5):420–425Crossref, Google Scholar
- A Procrustes problem on the Stiefel manifold. Numer. Math. (1999) 82(4):599–619Crossref, Google Scholar
- Kronecker Products and Matrix Calculus: With Applications (1981) (Halsted Press, Toronto) Google Scholar
- Positive definite completions of partial Hermitian matrices. Linear Algebra Appl. (1984) 58:109–124Crossref, Google Scholar
- Graph theoretic methods for matrix completion problems. Linear Algebra Appl. (2001) 328(1–3):161–202Crossref, Google Scholar
- Generalizations of Slater's constraint qualification for infinite convex programs. Math. Programming (1992) 57(1, Ser. B):85–101Crossref, Google Scholar
- Matrix completion problems: A survey. Proc. Sympos. Appl. Math. (1990) 40(American Mathematical Society, Providence, RI) 171–198Crossref, Google Scholar
- , Pardalos P. M., Wolkowicz H. Semidefinite programming and graph equipartition. Topics in Semidefinite and Interior-Point Methods (1998) 18(American Mathematical Society, Providence, RI) 77–96Fields Institute Communications SeriesCrossref, Google Scholar
- Semidefinite facial reduction for low-rank euclidean distance matrix completion. (2010) . Doctoral dissertation, University of Waterloo, Waterloo, Ontario, CanadaGoogle Scholar
- Explicit sensor network localization using semidefinite representations and facial reductions. SIAM J. Optim. (2010) 20(5):2679–2708Crossref, Google Scholar
- , Brezinski C., Zhang F. Eigenvalue and singular value inequalities of Schur complements. The Schur Complement and Its Applications, Numerical Methods and Algorithms (2005) 4(Springer-Verlag, New York) 47–82Crossref, Google Scholar
- Estimating bounds for quadratic assignment problems associated with the Hamming and Manhattan distance matrices based on semidefinite programming. SIAM J. Optim. (2010) 20(6):3408–3426Crossref, Google Scholar
- Semidefinite programming relaxations of nonconvex quadratic optimization. Handbook of Semidefinite Programming: Theory, Algorithms, and Applications (2000) 27(Kluwer Academic Publishers, Boston) 361–419International Series in Operations Research and Management ScienceCrossref, Google Scholar
- Schur complements and statistics. Linear Algebra Appl. (1981) 36:187–295Crossref, Google Scholar
- Semidefinite approximations for quadratic programs over orthogonal matrices. J. Global Optim. (2010) 48(3):447–463Crossref, Google Scholar
- Convex Analysis. Princeton Landmarks in Mathematics (1997) (Princeton University Press, Princeton, NJ) Google Scholar
- A generalized solution of the orthogonal Procrustes problem. Psychometrika (1966) 31(1):1–10Crossref, Google Scholar
- Theory of semidefinite programming for sensor network localization. Math. Programming (2007) 109(2–3, Ser. B):367–384Crossref, Google Scholar
- Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. (1995) 5(2):286–313Crossref, Google Scholar
- Further relaxations of the semidefinite programming approach to sensor network localization. SIAM J. Optim. (2008) 19(2):655–673Crossref, Google Scholar
- , Powell M. J. D., Scholtes S. Semidefinite and Lagrangian relaxations for hard combinatorial problems. Proc. 19th IFIP TC7 Conf. System Modelling Optim. (2000) (Kluwer Academic Publishers, Boston) 269–309Crossref, Google Scholar
- Semidefinite programming relaxations for the graph partitioning problem. J. Discrete Appl. Math. (1999) 96/97(1):461–479Crossref, Google Scholar
- Semidefinite programming relaxations for the quadratic assignment problem. J. Combin. Optim. (1998) 2(1):71–109Crossref, Google Scholar

