On the Convergence Rate for Stochastic Approximation in the Nonsmooth Setting

References

• Andradóttir S. A method for discrete stochastic optimization. Management Sci. (1995) 41:1946–1961Link, Google Scholar
• Benaïm M. Dynamics of stochastic approximation algorithms. Séminaire de Probabilités XXXIII (1999) (Springer-Verlag, Berlin) 1–68Lecture Notes in MathematicsCrossref, Google Scholar
• Benaïm M., Hirsch M. W. Asymptotic pseudotrajectories and chain recurrent flows, with applications. J. Dynam. Differential Equations (1996) 8:141–176Crossref, Google Scholar
• Benaïm M., Hofbauer J., Sorin S. Stochastic approximations and differential inclusions. SIAM J. Control Optim. (2005) 44:328–348Crossref, Google Scholar
• Benveniste A., Métivier M., Priouret P.Adaptive Algorithms and Stochastic Approximations (1990) (Springer-Verlag, New York) Crossref, Google Scholar
• Boyd S., Vandenberghe L. Subgradients. Lecture Notes (2008) . http://see.stanford.edu/materials/lsocoee364b/01-subgradients_notes.pdfGoogle Scholar
• Chung K. L. On a stochastic approximation method. Ann. Math. Statist. (1954) 25:463–483Crossref, Google Scholar
• Duflo M.Algorithmes Stochastiques (1996) (Springer, Berlin) Google Scholar
• Ermoliev Y. Stochastic quasigradient methods and their application to systems optimization. Stochastics (1983) 9:1–36Crossref, Google Scholar
• Fabian V. On asymptotic normality in stochastic approximation. Ann. Math. Statist. (1968) 39:1327–1332Crossref, Google Scholar
• Gelfand S. B., Mitter S. K. Simulated annealing with noisy or imprecise energy measurements. J. Optim. Theory Appl. (1989) 62:49–62Crossref, Google Scholar
• Kushner H., Yin G.Stochastic Approximation Algorithms and Applications (1997) (Springer-Verlag, New York) Crossref, Google Scholar
• Li Y. A martingale inequality and large deviations. Statist. Probab. Lett. (2003) 62:317–321Crossref, Google Scholar
• Lim E. Stochastic approximation over multidimensional discrete sets with applications to inventory systems and admission control of queueing networks. (2011) . PreprintGoogle Scholar
• Lu Y., Song J. S. Order-based cost optimization in assemble-to-order systems. Oper. Res. (2005) 53:151–169Link, Google Scholar
• Murota K. Note on multimodularity and L-convexity. Math. Oper. Res. (2005) 30:658–661Link, Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Sacks J. Asymptotic distribution of stochastic approximation procedures. Ann. Math. Statist. (1958) 29:373–405Crossref, Google Scholar
• Venter J. H. On Dvoretzky stochastic approximation theorems. Ann. Math. Statist. (1966) 37:1534–1544Crossref, Google Scholar
• Venter J. H. An extension of the Robbins-Monro procedure. Ann. Math. Statist. (1967) 38:181–190Crossref, Google Scholar