Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 4875-4880

  Yousefian, Farzad ^a   Nedić, Angelia ^a   Shanbhag, Uday V ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Local smoothing technique; Nondifferentiable convex minimization; Stochastic approximation method

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; OPTIMIZATION; STEEL BEAMS AND GIRDERS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CONVEX MINIMIZATION; LOCAL SMOOTHING; NON-DIFFERENTIABLE OPTIMIZATION; STOCHASTIC APPROXIMATION METHODS; STOCHASTIC APPROXIMATIONS; STOCHASTIC OPTIMIZATIONS; SUB-GRADIENT ALGORITHM; UNIFORM DISTRIBUTION;

ITERATIVE METHODS;

EID: 77957824010     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5530908     Document Type: Conference Paper

References (22)

1. H. Robbins and S. Monro, "A stochastic approximation method," Ann. Math. Statistics, vol. 22, pp. 400-407, 1951.
2. Y. M. Ermoliev, "On the stochastic quasi-gradient method and stochastic quasi-feyer sequences," Kibernetika, Kiev, no. 2, pp. 73-83, 1969.
3. -, Stochastic Programming Methods. Nauka, Moscow, 1976.
4. -, "Stochastic quasigradient methods and their application to system optimization," Stochastic, vol. 9, pp. 1-36, 1983.
5. -, "Stochastic quasigradient methods," in Numerical Techniques for Stochastic Optimization. Sringer-Verlag, 1983, pp. 141-185.
6. B. Polyak, Introduction to optimization. New York: Optimization Software, Inc., 1987.
7. B. T. Polyak and A. B. Juditsky, "Acceleration of stochastic approximation by averaging," SIAM J. Control Optim., vol. 30, no. 4, pp. 838-855, 1992.
8. A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, "Robust stochastic approximation approach to stochastic programming," SIAM Journal on Optimization, vol. 19, no. 4, pp. 1574-1609, 2009.
9. A. Nedić, "Subgradient methods for convex minimization," Ph.D. dissertation, MAssachussetts Institute of Technology, 2001.
10. A. Nedićand D. P. Bertsekas, "Convergence rate of incremental algorithms," Stochastic Optimization: Algorithms and Applications, pp. 223-264, 2001.
11. S. S. Ram, A. Nedić, and V. V. Veeravalli, "Incremental stochastic subgradient algorithms for convex optimization," SIAM Journal on Optimization, vol. 20, no. 2, pp. 691-717, 2009.
12. -, "Distributed stochastic subgradient projection algorithms for convex optimization," 2009, submitted.
13. -, "Asynchronous gossip algorithms for stochastic optimization," 2009, accepted in IEEE Conference on Decision and Control.
14. H. Jiang and H. Xu, "Stochastic approximation approaches to the stochastic variational inequality problem," IEEE Transactions Automatic Control, vol. 53, no. 6, pp. 1462-1475, 2008.
15. D. P. Bertsekas and J. N. Tsitsiklis, "Gradient convergence in gradient methods," SIAM Journal on Optimization, vol. 10, no. 3, pp. 627-642, 2000.
16. V. S. Borkar and S. P. Meyn, "The O.D.E. method for convergence of stochastic approximation and reinforcement learning," SIAM J. Control Optim., vol. 38, no. 2, pp. 447-469 (electronic), 2000.
17. V. S. Borkar, Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press, 2008.
18. H. Lakshmanan and D. Farias, "Decentralized recourse allocation in dynamic networks of agents," SIAM Journal on Optimization, vol. 19, no. 2, pp. 911-940, 2008.
19. D. P. Bertsekas, "Stochastic optimization problems with nondifferentiable functionals with an application in stochastic programming," in Proceedings of 1972 IEEE Conference on Decesion and Control, 1972, pp. 555-559.
20. -, "Stochastic optimization problems with nondifferentiable cost functionals," Journal of Optimization Theory and Applications, vol. 12, no. 2, pp. 218-231, 1973.
21. R. T. Rockafellar, Convex Analysis. Princeton, New Jersey: Princeton University Press, 1970.
22. V. Strassen, "The existence of probability measures with given marginales," Annals of Mathematical Statistics, vol. 38, pp. 423-439, 1965.