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In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem.
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C. Helmberg and F. Rendl, A Spectral Bundle Method for Semidefinite Programming , SIAM Journal on Optimization 10
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F. Oustry, A second-order bundle method to minimize the maximum eigenvalue function , Mathematical Programming 89
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A. Nemirovski, Prox-Method with Rate of Convergence O ( 1 / t ) O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems , SIAM Journal on Optimization 15
2004
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A. Ben-Tal and A. Nemirovski, Non-Euclidean restricted memory level method for large-scale convex optimization , Mathematical Programming 102
2005
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K. Tsuda, G. Rätsch, and M. K. Warmuth, Matrix exponentiated gradient updates for on-line learning and bregman projections , Journal of Machine Learning Research 6
2005
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M. K. Warmuth and D. Kuzmin, Online variance minimization , In Proceedings of the 19th Annual Conference on Learning Theory, Springer, 2006, pp. 514–528
2006
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S. Arora and S. Kale, A combinatorial, primal-dual approach to semidefinite programs , Proceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, California, USA, June 2007 (D. Johnson and U. Feige, eds.), ACM, 2007, pp. 227–236
2007
Cited alongside, same era.
Y. Nesterov, Smoothing technique and its applications in semidefinite optimization , Mathematical Programming 110
2007
Later among the works it cites.
A. d’Aspremont, Smooth optimization with approximate gradient , SIAM Journal on Optimization 19
2008
Later among the works it cites.
A. d’Aspremont, Subsampling Algorithms for Semidefinite Programming , Tech. report, March 2008, Available at http://www.princeton.edu/ ∼ \sim aspremon/ColSubSamp.pdf
2008
Later among the works it cites.
A. Juditsky, A. Nemirovski, and C. Tauvel, Solving Variational Inequalities with Stochastic Mirror-Prox Algorithm , Tech. report, 2008, Available at http://www2.isye.gatech.edu/ ∼ \sim nemirovs/SMP.pdf
2008
Later among the works it cites.
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