Fetching the paper…
Reading the bibliography…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator.
Robbins, H. and Monro, S., (1951) A Stochastic Approximation Method, The Annals of Mathematical Statistics , Vol. 22, pp. 400–407
1951
Earlier work this paper cites.
Polyak, B.T. (1969) Minimization of unsmooth functionals, USSR Computational Matematics and Mathematical Physics , Vol. 9, pp. 14–29
1969
Earlier work this paper cites.
Robbins, H. and Siegmund, D.O., (1971) A convergence theorem for nonnegative almost super-martingales and some applications, Optimizing Methods in Statistics , pp. 233–257
1971
Earlier work this paper cites.
Korpelevich, G.M. (1976) The extragradient method for finding saddle points and other problems, Ekonomika i Matematcheskie Metody , Vol. 12, pp. 747–756
1976
Earlier work this paper cites.
Kibardin, V.M (1980) Decomposition into functions in the minimization problem, Automatic and Remote Control , Vol. 40, pp. 1311–1323
1980
Earlier work this paper cites.
Censor, Y. (1981) Row-action methods for huge and sparse systems and its applications, SIAM Review , Vol. 23, pp. 444-464
1981
Earlier work this paper cites.
Fukushima, M., (1986) A relaxed projection method for variational inequalities, Mathematical Programming , Vol. 35, pp. 58–70
1986
Earlier work this paper cites.
Polyak, B. (1987) Introduction to Optimization , Optimization Software, New York
1987
Earlier work this paper cites.
Burke, J.V. and Ferris, M.C. (1993) Weak sharp minima in mathematical programming, SIAM Journal on Control and Optimization , Vol. 31, pp. 1340–1359
1993
Earlier work this paper cites.
Luo, Z.-Q., Tseng, P. (1994) Analysis of an approximate gradient projection method with applications to the backpropagation algorithm, Optimization Methods and Softawre , Vol. 4, pp. 85–101
1994
Earlier work this paper cites.
Bauschke, H.H. and Borwein, J.M. (1996) On projection algorithms for solving convex feasibility problems, SIAM Review , Vol. 38, pp. 367–426
1996
Earlier work this paper cites.
Iusem, A.N. and Svaiter, B.F. (1997) A variant of Kopelevich’s method for variational inequalities with a new search strategy, Optimization , Vol. 42, pp.309–321
1997
Earlier work this paper cites.
Pang, J.-S. (1997) Error bounds in mathematical programming, Mathematical Programming , Vol. 79, pp. 299–332
1997
Earlier work this paper cites.
Iusem, A.N. (1998) On some properties of paramonotone operators, Journal of Convex Analysis , Vol. 5, pp. 269–278
1998
Earlier work this paper cites.
Marcotte, P. and Zhu, D. (1998) Weak sharp solutions of variational inequalities, SIAM Journal on Optimization , Vol. 9, pp. 179–189
1998
Earlier work this paper cites.
Rockafellar, R.T. and Wets, R.J-B. (1998) Variational Analysis , Springer, Berlin
1998
Cited alongside, same era.
Gürkan, G., Özge, A.Y. and Robinson, S.M. (1999) Sample-path solution of stochastic variational inequalities, Mathematical Programmming , Vol. 84, pp. 313–333
1999
Cited alongside, same era.
Bauschke, H.H. (2001) Projection algorithms: results and open problems. In: Butnariu, D., Censor, Y., Reich, Y. (eds.) Inherently Parallel Algorithms in Feasibility and Optimization and their Applications , Elsevier, Amsterdam, pp. 11–22
2001
Cited alongside, same era.
Nedić, A., Bertsekas, D.P. (2001) Incremental subgradient method for nondifferentiable optimization, SIAM Journal on Optimization , Vol. 12, pp. 109–138
2001
Cited alongside, same era.
Polyak, B.T. (2001) Random algorithms for solving convex inequalities, In: Butnariu, D., Censor, Y., Reich, S. (eds.) Inherently Parallel Algorithms in Feasibility and Optimization and their Applications , pp. 409–422. Elsevier, Amsterdam
Bello Cruz, J.Y. and Iusem, A.N., (2010) Convergence of direct methods for paramonotone variational inequalities, Computational Optimization and Applications , Vol. 46, pp. 247–263
2010
Later among the works it cites.
Bach, F. and Moulines, E. (2011) Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning, Advances in Neural Information Processing Systems (NIPS)
2011
Later among the works it cites.
Bertsekas, D.P. (2011) Incremental proximal methods for large scale convex optimization, Mathematical Programming , Vol. 129, pp. 163–195
2011
Later among the works it cites.
Juditsky, A., Nemirovski, A. and Tauvel, C. (2011) Solving variational inequalities with stochastic mirror-prox algorithm, Stochastic Systems , Vol. 1, pp. 17–58
2011
Later among the works it cites.
Nedić, A. (2011) Random algorithms for convex minimization problems, Mathematical Programming , Vol. 129, pp. 225–253
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2001
Cited alongside, same era.
Bauschke, H.H., Combettes, H.H., Luke, D.R. (2003) Hybrid projection-reflection method for phase retrieval, Journal of the Optical Socety of America , Vol. A20, pp. 1025–1034
2003
Cited alongside, same era.
Facchinei, F. and Pang, J.-S. (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems , Springer, New York
2003
Cited alongside, same era.
Nemirovski, A. (2004) 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 Journal on Optimization , Vol. 15, pp. 229–251
2004
Cited alongside, same era.
Auslender, A. and Teboulle, M. (2005) Interior projection-like methods for monotone variational inequalities, Mathematical Programming, Ser. A , Vol. 104, pp. 39–68
2005
Cited alongside, same era.
Cegielski, A., Suchocka, A. (2008) Relaxed alternating projection methods. SIAM Journal on Optimization , Vol. 19, pp. 1093-1106
2008
Cited alongside, same era.
Censor, Y. and Gibali, A. (2008) Projections onto super-half-spaces for monotone variational inequality problems in finite-dimensional spaces, Journal of Nonlinear and Convex Analysis , Vol. 9, pp. 461–474
2008
Cited alongside, same era.
Deutsch, F. and Hundal, H., (2008) The rate of convergence for the cyclic projections algorithm III: regularity of convex sets, Journal of Approximation Theory , Vol. 155, pp. 155–184
2008
Cited alongside, same era.
2011
Later among the works it cites.
Bello Cruz, J.Y. and Iusem, A.N. (2012) An explicit algorithm for monotone variational inequalities, Optimization , Vol. 61, pp. 855–871
2012
Later among the works it cites.
Chen, X., Wets, R.J-B and Zhang, Y. (2012) Stochastic variational inequalities: residual minimization smoothing sample average approximations, SIAM Journal on Optimization , Vol. 22, pp. 649–673
2012
Later among the works it cites.
Kannan, A. and Shanbhag, U.V. (2012) Distributed computation of equilibria in monotone Nash games via iterative regularization techniques, SIAM Journal on Optimization , 22, pp. 1177–1205
2012
Later among the works it cites.
Koshal, J., Nedić, A. and Shanbhag, U.V. (2013) Regularized iterative stochastic approximation methods for stochastic variational inequality problems, IEEE Transactions on Automatic Control , Vol 58, pp. 594–608
2013
Later among the works it cites.
Chen, Y., Lan, G. and Ouyang, Y. Accelerated schemes for a class of variational inequalities, pre-print. http://www.ise.ufl.edu/glan/files/2014/03/AMP3-17-14.pdf
2014
Later among the works it cites.
2014
Later among the works it cites.
Bello Cruz, J.Y. and Iusem A.N. (2015) Full convergence of an approximate projections method for nonsmooth variational inequalities, Mathematics and Computers in Simulation , Vol. 114, pp. 2–13
2015
Later among the works it cites.
Wang, M. and Bertsekas, D. (2015) Incremental Constraint Projection Methods for Variational Inequalities, Mathematical Programmming , Vol. 150, pp. 321–363
2015
Later among the works it cites.
Wang, M. and Bertsekas, D. (2016) Stochastic first-order methods with random constraint projection, SIAM Journal on Optimization , Vol. 26, pp. 681-717
2016
Later among the works it cites.