Stochastic Variational Analysis

Stochastic Variational Analysis

[ 32] X. Chen, H. Sun and R. Wets, Regularized mathematical programs with stochastic

equilibrium constraints: estimating structural demand models. SIAM J. on Optimization,

(to appear, 2014). Tech. Report PolyUniversity, Hong Kong, 2013.

[ 31] V. Norkin and R. Wets, On strong graphical law of large numbers for random

semicontinuous mappings, Vestnik of Saint-Petersburg University, Serial 10, pp. 102-110

[ 30] V.Norkin and R. Wets, Law of small numbers as concentration inequalities for sums of

independent random sets and random set valued mappings. In

Skalauskas, A. Tomagard and S. Wallace, editors, Stochastic programming for

Implementation and Advanced Applications, pages 94-99. The Association of Lithuanian

Serials, 2012

[ 29] R. Wets, Stochastic variational analysis, Mini-Course at ETH-Zurich, May 2012,

[ 28] X. Chen, R. Wets and Y. Zhang, Stochastic variational inequalities: residual minimization,

smoothing/sample average approximations, SIAM J. on Optimization, 22:649-673,2012

[ 27] R. Wets. Stochastic variational analysis. Tutorial: October meeting

“Computing with Uncertainty”, Institute of Mathematics and its Applications, 2010

http://www.ima.umn.edu/2010-2011/T10.16-17.10/activities/Wets-Roger/wetsTutorial.pdf.

[ 26] V. Norkin, R. Wets, and H. Xu. Graphical convergence of sample average random

set-valued mappings. Mathematics, University of California, Davis, 2010.

[ 25] W. Römisch and R. Wets. Stability of ε-approximate solutions to convex stochastic

programs. SIAM Journal on Optimization, 18:961–979, 2007.

[ 24] L.A. Korf and R. Wets. An ergodic theorem for stochastic programming problems.

In V.H. Nguyen, J.J. Strodiot, and P. Tossings, editors, Proceedings of the 9th

Belgian-French-German Conference on Optimization,

vol. 481 of Lecture Notes in Economics and Mathematical Sciences,

pages 203–217. Springer, 2001.

[ 23] L. Korf and R. Wets. Random lsc functions: an ergodic theorem.

Mathematics of Operations Research, 26:421–445, 2001.

[ 22] L.A. Korf and R. Wets. Random lsc functions: Kolmogorov’s extension theorem.

Stochastic Programmin E-Prints Series, 2000. http://dochost.rz.hu-berlin.de/speps/.

[ 21] L.A. Korf and R. Wets. Random lsc functions: scalarization.

Stochastic Programmin E-Prints Series, 2000. http://dochost.rz.hu-berlin.de/speps/.

[ 20] Z. Artstein and R. Wets. Consistency of minimizers and the SLLN for stochastic

programs. Journal of Convex Analysis, 2:1–17, 1995.

[ 19] Y.M. Kaniovski, A.J. King, and R. Wets. Probabilistic bounds (via large deviations) for the

solutions of stochastic programming problems.

Annals of Operations Research, 56:189–208, 1995.

[ 18] R. Lucchetti, G. Salinetti, and R. Wets. Uniform convergence of probability measures:

topological criteria. Journal of Multivariate Analysis, 51:252–264, 1994.

[ 17] R. Lucchetti and R. Wets. Convergence of minima of integral functionals, with

applications to optimal control and stochastic optimization. Statistics and Decisions,

11:69-84, 1993.

[16] G. Salinetti and R. Wets. Glivenko-Cantelli type theorems: an application of the

convergence theory of stochastic suprema.

Annals of Operations Research, 30:157–168, 1991.

[ 15] R. Wets. Laws of large numbers for random lsc functions.

Applied Stochastic Analysis & Stochastics Monographs, 5:101–120, 1991.

[ 14] H. Attouch and R. Wets. Epigraphical processes: laws of large numbers for random lsc

functions. Séminaire d’Analyse Convexe, 13:13.1–13.29, 1991.

[ 13] A.J. King and R. Wets. Epi-consistency of convex stochastic programs.

Stochastics and Stochastics Reports, 34:83–92, 1990.

[ 12] G. Salinetti and R. Wets. Random semicontinuous functions. In L.M. Ricciardi, editor,

Lectures in Applied Mathematics and Informatics, pages 330–353.

Manchester University Press, 1990.

[ 11] Z. Artstein and R. Wets. Decentralized allocation of resources among many agents.

Journal of Mathematical Economics, 18:303–324, 1989.

[ 10] Z. Artstein and R. Wets. Approximating the integral of a multifunction.

Journal of Multivariate Analysis, 24:285–308, 1988.

[ 9] J. Dupačová and R. Wets. Asymptotic behavior of statistical estimators and of optimal

solutions for stochastic optimization problems.

The Annals of Statistics, 16:1517–1549, 1988.

[ 8] G. Salinetti and R. Wets. Weak convergence of probability measures revisited.

Technical report, International Institute of Systems Analysis, Laxenburg, 1987.

IIASA WP-87-30.

[ 7] G. Salinetti, W. Vervaat, and R. Wets. On the convergence in probability of random sets

(measurable multifunctions). Mathematics of Operations Research, 11:420–422, 1986.

[ 6] G. Salinetti and R. Wets. On the convergence in distribution of measurable multifunctions

(random sets), normal integrands, stochastic processes and stochastic infima.

Mathematics of Operations Research, 11:385–419, 1986.

[ 5] G. Salinetti and R. Wets. On the hypo-convergence of probability measures.

In R. Conti, E. De Giorgi, and F. Giannessi, editors, Optimization and Related Fields.

Erice 1984, pages 371–395. Springer Lecture Notes in Mathematics 1190, 1986.

[ 4] S.D. Flåm and R. Wets. Finite horizon approximates of infinite horizon stochastic

programs. In V. Arkin, A. Shiraev, and R. Wets, editors, Stochastic Optimization,

vol. 81 Lecture Notes in Control and Information Sciences, pages 337–350. Springer, 1986.

[ 3] R.T. Rockafellar and R. Wets. On the interchange of subdifferentiation and conditional

expectation for convex functionals. Stochastics, 7:173–182, 1982.

[ 2] G. Salinetti and R. Wets. On the convergence of closed-valued measurable

multifunctions. Transactions of the American Mathematical Society, 266:275-289, 1981

[ 1] R. Wets. On the convergence of random convex sets. In A. Auslander, editor,

Convex Analysis and Its Applications, pages 191–206. Springer, 1977.