Regularization methods for semidefinite programming

SIAM Journal on Optimization

Volumn 20, Issue 1, 2009, Pages 336-356

  Malick, Jérôme ^a   Povh, Janez ^b   Rendl, Franz ^c   Wiegele, Angelika ^c  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF MARIBOR   (Slovenia)

^c UNIVERSITY OF KLAGENFURT   (Austria)

Author keywords

Augmented Lagrangian method; Large scale semidefinite problems; Regularization methods; Semidefinite programming

Indexed keywords

AUGMENTED LAGRANGIAN METHODS; AUGMENTED LAGRANGIANS; BOUNDARY POINT METHOD; PRACTICAL IMPLEMENTATION; REGULARIZATION METHODS; SEMI-DEFINITE PROGRAMMING;

CONVEX OPTIMIZATION; DYNAMIC LOADS;

LAGRANGE MULTIPLIERS;

EID: 70450212537     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/070704575     Document Type: Article

References (33)

1. K. ARROW, L. HURWICZ, AND H. UZAWA, Studies in Linear and Nonlinear Programming, Stanford University Press, 1959.
2. D. P. BERTSEKAS, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.
3. R. BELLMAN, R. KALABA, AND J. LOCKETT, Numerical Inversion of the Laplace Transform, Elsevier, New York, 1966.
4. S. BURER AND R. D. C. MONTEIRO, A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization, Math. Program. (Series B), 95 (2003), pp. 329-357.
5. S. BURER AND D. VANDENBUSSCHE, Solving lift-and-project relaxations of binary integer programs, SIAM J. Optim., 16 (2006), pp. 726-750.
6. I. DUKANOVIC AND F. RENDL, Semidefinite programming relaxations for graph coloring and maximal clique problems, Math. Program., 109 (2007), pp. 345-365.
7. M. R. HESTENES, Multiplier and gradient methods, J. Optim. Theory Appl., 4 (1969), pp. 303-320.
8. N. HIGHAM, Computing a nearest symmetric correlation matrix - a problem from finance, IMA J. Numer. Anal., 22 (2002), pp. 329-343.
9. C. HELMBERG AND F. RENDL, A spectral bundle method for semidefinite programming, SIAM J. Optim., 10 (2000), pp. 673-696.
10. J.-B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms, Springer Verlag, Heidelberg, 1993. Two volumes.
11. F. JARRE AND F. RENDL, An augmented primal-dual method for linear conic problems, SIAM J. Optim., 19 (2008), pp. 808-823.
12. D. J. JOHNSON AND M. A. TRICK, EDS., Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993, American Mathematical Society, Boston, MA, 1996.
13. M. KOČVARA AND M. STINGL, On the solution of large-scale SDP problems by the modified barrier method using iterative solvers, Math. Program., 109 (2007), pp. 413-444.
14. Z. LU, A. NEMIROVSKI, AND R. D. C. MONTEIRO, Large-scale semidefinite programming via a saddle point Mirror-Prox algorithm, Math. Program., 109 (2007), pp. 211-237.
15. L. LOVÁSZ, On the shannon capacity of a graph, IEEE Trans. Inform. Theory, 25 (1979), pp. 1-7.
16. J. MALICK, A dual approach to semidefinite least-squares problems, SIAM J. Matrix Anal. Appl., 26 (2004), pp. 272-284.
17. J. MALICK, Algorithmique en Analyse Variationnelle et Optimisation Semidéfinie, Ph. D. thesis, Université Joseph Fourier de Grenoble (France), November 25, 2005.
18. B. MARTINET, Régularisation d'inéquations variationnelles par approximations succes-sives, Revue Française d'Informatique et Recherche Opérationnelle, R-3 (1970), pp. 154-179.
19. D. MITTELMANN, An independent benchmarking of sdp and socp solvers, Math. Program. B, 95 (2003), pp. 407-430.
20. R. D. C. MONTEIRO, First- and second-order methods for semidefinite programming, Math. Program., 97 (2003), pp. 663-678.
21. M. J. D. POWELL, A method for nonlinear constraints in minimization problems, in Optimization, R. Fletcher, ed., Academic Press, London, New York, 1969.
22. J. POVH, F. RENDL, AND A. WIEGELE, A boundary point method to solve semidefinite programs, Computing, 78 (2006), pp. 277-286.
23. B. T. POLYAK AND N. V. TRETJAKOV, On an iterative method for linear programming and its economical interpretations, Ékonom. i Mat. Methody, 8 (1972), pp. 740-751.
24. H. QI AND D. SUN, Quadratic convergence and numerical experiments of Newton's method for computing the nearest correlation matrix, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 360-385.
25. F. RENDL, A boundary point method to solve semidefinite programs, Report 2/2005, Annals of Oberwolfach, Springer, Berlin, 2005.
26. R. T. ROCKAFELLAR, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 1 (1976), pp. 97-116.
27. R. T. ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), pp. 877-898.
28. A. SCHRIJVER, A comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory, IT-25 (1979), pp. 425-429.
29. M. J. TODD, Semidefinite optimization, Acta Numer., 10 (2001), pp. 515-560.
30. K. C. TOH, Solving large scale semidefinite programs via an iterative solver on the augmented systems, SIAM J. Optim., 14 (2004), pp. 670-698.
31. Website, http://www.math.uni-klu.ac.at/or/software.
32. H. WOLKOWICZ, R. SAIGAL, AND L. VANDENBERGHE, Handbook of Semidefinite Programming, Kluwer, Norwell, MA, 2000.
33. X. ZHAO, D. SUN, AND K. TOH, A Newton-CG augmented Lagrangian method for semidefinite programming, Technical report, National University of Singapore, March 2008.