Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem

Automation and Remote Control

Volumn 72, Issue 2, 2011, Pages 342-352

  Nazin, A V ^a   Polyak, B T ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MULTI AGENT SYSTEMS; OPTIMIZATION; SEARCH ENGINES; STOCHASTIC SYSTEMS;

CONVERGENCE RATES; DESCENT METHOD; NETWORK CONTROL; NUMBER OF ITERATIONS; RANDOMIZED ALGORITHMS; STOCHASTIC MATRICES; STOCHASTIC OPTIMIZATIONS; UPPER BOUNDARY;

MATRIX ALGEBRA;

EID: 79954495351     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0005117911020111     Document Type: Article

References (14)

1. S. Brin L. Page 1998 The Anatomy of a Large-scale Hypertextual WEB Search Engine Comput. Network ISDN Syst. 30 1-7 107 117
2. Langville, A.N. and Meyer, C.D., Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton: Princeton Univ. Press, 2006.
3. Ishii, H. and Tempo, R., A Distributed Randomized Approach for the PageRank Computation, Parts 1, 2, in Proc. 47th IEEE Conf. Decision Control, Cancun, Mexico, 2008, pp. 3523-3528, 3529-3534.
4. Tempo, R., Calafiore, G., and Dabbene, F., Randomized Algorithms for Analysis and Control of Uncertain Systems: An Overview, in Lecture Notes in Control and Information Sciences, Berlin: Springer, 2005, vol. 268/2001, p. 344.
5. A.V. Nazin B.T. Polyak 2009 Randomized Algorithm for Finding Eigenvector of Stochastic Matrix with Application to PageRank Dokl. Ross. Akad. Nauk 426 6 734 737 2573029
6. Nazin, A.V. and Polyak, B.T., Adaptive Randomized Algorithm for Finding Eigenvector of Stochastic Matrix with Application to PageRank, in 48th IEEE Conf. Decision Control, Shanghai, P.R. China, December 16-18, 2009.
7. Nemirovskii, A.S. and Yudin, D.B., Slozhnost' zadach i effektivnost' metodov optimizatsii, Moscow: Nauka, 1979. Translated under the title Problem Complexity and Method Efficiency in Optimization, New York: Wiley, 1983.
8. Yu. Nesterov 2005 Primal-Dual Subgradient Methods for Convex Problems Math. Program. 103 1 127 152 2166537 1079.90102
9. A.B. Yuditskii A.V. Nazin A.B. Tsybakov N. Vayatis 2005 Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging Probl. Inform. Transm. 41 4 368 384 2198228 (Pubitemid 43141959)
10. Juditsky, A., Lan, G., Nemirovski, A., and Shapiro, A., Stochastic Approximation Approach to Stochastic Programming, SIAM J. Optim., 2007 ( http://www.optimization-online.org/DB-HTML/2007/09/1787.html ).
11. Juditsky, A., Nemirovski, A., and Tauvel, C., Solving Variational Inequalities with Stochastic Mirror-Prox Algorithm, SIAM J. Optim., 2008 ( http://arxiv.org/abs/0809.0815v1 ).
12. Nazin, A.V., Solution to a Particular Deterministic Problem in Finite High Dimension by the Recursive Randomized Mirror Descent Algorithm, in 8th Meeting Math. Statist., CIRM, Luminy, France, December 15-19, 2008 ( http://www.cirm.univ-mrs.fr ).
13. Rockafellar, R.T. and Wets, R.J.B., Variational Analysis, New York: Springer, 1998.
14. Ben-Tal, A. and Nemirovski, A., Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Philadelphia: SIAM, 2001.