Large-scale semidefinite programming via a saddle point Mirror-Prox algorithm

Mathematical Programming

Volumn 109, Issue 2-3, 2007, Pages 211-237

  Lu, Zhaosong ^a   Nemirovski, Arkadi ^b   Monteiro, Renato D C ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b Georgia Institute of Technology   (United States)

Author keywords

Mirror Prox method; Saddle point problem; Semidefinite programming

Indexed keywords

LINEAR PROGRAMMING; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING;

MIRROR PROX METHODS; POSITIVE SEMIDEFINITENESS; SADDLE POINT PROBLEMS; SEMIDEFINITE PROGRAMMING;

ALGORITHMS;

EID: 33846655826     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0031-2     Document Type: Conference Paper

References (8)

1. Burer, S., Monteiro, R.D.C., Zhang, Y.: Solving a class of semidefinite programs via nonlinear programming. Math. Program. 93, 97-122 (2002)
2. Burer, S., Monteiro, R.D.C.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. Ser. B 95, 329-357 (2003)
3. Fukuda, M., Kojima, M., Murota, K., Nakata, K.: Exploiting sparsity in semidefinite programming via matrix completion I: general framework. SIAM J Optim. 11, 647-674 (2000)
4. Grone, B., Johnson, C.R. Marques de Sa, E., Wolkowicz, H.: Positive definite completions of partial Hermitian matrices. Linear Algebr. Appl. 58, 109-124 (1984)
5. Helmberg, C., Rendl, F.: A spectral bundle method for semidefinite programming. SIAM J. Optim. 10, 673-696 (2000)
6. Nemirovski, A.: Prox-method with rate of convergence O(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15, 229-251 (2004)
7. Nesterov, Yu.: Smooth minimization of non-smooth functions. Math. Program. 103, 127-152 (2005)
8. Nesterov, Yu.: Dual extrapolation and its applications for solving variational inequalities and related problems. - CORE Discussion Paper 2003/68, http://www.core.ucl.ac.be/services/COREdp03.html (2003)