Stochastic Optimization

Stochastic Optimization

[112] C. Kuhlmann, D. Martel, R. Wets and D. Woodruff, Generating stochastic ellipsoidal

forest and wildland fire scar scenarios for strategic forest management planning under

uncertainty. Forest Sciences, 60 (2014), 15 pages

[111] D. Gade, G. Hackebeil, S. Ryan, J.-P. Watson, R. Wets and D. Woodruff. Obtaining

lower bounds from the Progressive Hedging algorithm for stochastic mixed-integer

programs. Mathematical Programming, 2013 (submitted).

[110] K. Cheung, Y. Feng, D. Gade, Y. Lee, C. Monroy, I. Rios, F. Rüdel, S. Ryan, J.-P.

Watson, R. Wets and D. Woodruff. Stochastic Unit Commitment at ISO scale: an ARPAe

projectf. 2014 IEEE Power & Energy Society General Meeting Proceedings, 2014

[109] K. Cheung, D. Gade, C. Monroy, S. Ryan, J.-P. Watson, R. Wets and D. Woodruff.

Toward scalable stochastic unit commitment - Part 2: Assessing solver performance.

IEEE Transactions on Power Systems (submitted). 2013

[108] Y. Feng, I. Rios, S. Ryan, K. Spürkel, J.-P. Watson, R. Wets and D. Woodruff. Toward

scalable stochastic unit commitment - Part 1: load scenarios generation. IEEE

Transactions on Power Systems (submitted). 2013.

[107] I. Rios, R. Wets and D. Woodruff, Multi-period forecasting with limited information and

scenario generation with limited data. 2013 (submitted for publication)

[106] A. Weintraub and R. Wets. Harvesting management: generating wood-prices scenarios,

Tech. Report, Instituto Sistemas Complejos de Ingenieria, Univ. de Chile, 2013.

[105] R. Wets. Foreword “Stochastic Optimization” by P. Carpentier, J.-P. Chancelier, G. Cohen

and M. De Lara, Springer, 2013. (proposed but not included in book))

[104] S. Ryan, R. Wets, D. Woodruff, C. Monroy-Silva and J.-P. Watson, Toward scalable

Progressive Hedging for stochastic unit commitment. 2013 IEEE Power &

Energy Society General Meeting

[103] Y. Feng, D. Gade, S. Ryan, J.-P. Watson, R. Wets and D. Woodruff. A new

approximation method for generating day-ahead load scenarios. 2013 IEEE Power &

Energy Society General Meeting

[102] R. Wets. An Optimization Primer. AMS Graduate Texts or Springer (in progress), 2011.

[101] F. Badilla-Veliz, J.-P. Watson, A. Weintraub, R. Wets, and D. Woodruff. Stochastic

Optimization Models in Forest Planning: A progressive hedging approach. Annals of

Operations Research. 2014.

[100] J.-P. Watson, R. Wets, and D. Woodruff. Scalable heuristics for a class of

chance-constrained stochastic programs. INFORMS Journal on Computing,

22:543–554, 2010. [Video view: http://dx.doi.org/10.1287/ijoc.1090.0372]

[ 99] D. The Luc and R. Wets. Outer-semicontinuity of positive hull mappings with applications

to semi-infinite and stochastic programming.

SIAM Journal on Optimization, 19:700-713, 2008.

[ 98] S. Tian and R. Wets. Pricing contingent claims: a computational compatible approach.

Technical report, Mathematics, University of California, Davis, 2007.

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

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

[ 96] A. King, L. Somlý́ody, and R. Wets. Stochastic optimization for lake eutrophication

management. In S. Wallace and W. Ziemba, es, Applications of Stochastic Programming,

pages 333–361. SIAM-MPS Series in Optimization, 2004.

[ 95] R. Wets. Stochastic programming models: Wait-and-see versus here-and-now. In F.

Auzerais, R. Burridge, C. Greengard, and A. Ruszczynski, editors, Decision Making

under Uncertainty: Energy and Environmental Models, pages 1–16. Springer, 2001.

[ 94] R. Wets and W. T. Ziemba, editors. Stochastic Programming. State of the Art, 1998. Baltzer

Science Publishers, 1999.

[ 93] T.W. Jonsbråten, R. Wets, and D. L. Woodruff. A class of stochastic programs with

decision dependent random elements. Annals of Operations Research, 82:83–106, 1998.

[ 92] E. Polak, R. Wets, and A. der Kiureghian. On an approach to optimization problems with

a probabilistic cost and or constraints. In G. Di Pilo and F. Giannessi, editors, Nonlinear

Optimization and Applications 2, pages 223–251. Kluwer Academic Publishers, 1998.

[ 91] R. Wets. Stochastic programs with chance constraints: generalized convexity and

approximation issues. In J.-P. Crouzeix, J.E. Martinez-Legaz, and M. Volle, editors,

Generalized Convexity, Generalized Monotonicity: Recent Results, pages 61–74. Kluwer, 1998.

[ 90] R. Wets. Challenges in stochastic programming.

Mathematical Programming, 75:115–136, 1996.

[ 89] Z. Artstein and R. Wets. Stability results for stochastic programs and sensors, allowing for

discontinuous objective functions. SIAM J. on Optimization, 4:537–550, 1995.

[ 88] H. Vladimirou, S. Zenios, and R. Wets, editors. Models for Planning under Uncertainty.

Baltzer Science Publishers, 1995.

[ 87] R. Wets. Interview: G.B. Dantzig Prize. Optima, 46:3–5, 1995.

[ 86] 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.

[ 85] G B. Andreatta, G. Salinetti, and R. Wets, editors. Stochastic Programming. Proceedings

Symposium Udine. J.C. Baltzer AG, 1995.

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

J. of Convex Analysis, 2:1–17, 1995.

[ 83] R. Wets and A.J. King. Lectures on stochastic programming.

Scandinavian Graduate Course, Nordseter, 1994.

[ 82] C. Claessens, J. Kreuser, L. Seigel, and R. Wets. A risk management model to assist

developing countries in hedging against interest rate, commodity price and exchange rate

fluctuations. Technical report, The World Bank, Washington D.C., 1994.

[ 81] A.J. King and R. Wets. Stochastic programming. SIAG/OPT Views-and-News, 4, 1994.

[ 80] L.F. Escudero, P.V. Kamesan, A.J. King, and R. Wets. Aggregate production planning and

sourcing decisions via scenario modeling.

Annals of Operations Research, 43:311–336, 1993.

[ 79] Z. Artstein and R. Wets. Sensors and information in optimization under stochastic

uncertainty. Mathematics of Operations Research, 18:523– 547, 1993.

[ 78] S.W. Wallace and R. Wets. Preprocessing in stochastic programming: the case of

capacitated networks. ORSA J. on Computing, 5, 1993.

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

to optimal control and stochastic optimization. Statistics and Decisions, 11, 1993.

[ 76] R.T. Rockafellar and R. Wets. A dual strategy for the implementation of the aggregation

principle in decision making under uncertainty. Applied Stochastic Models and Data Analysis,

8:245–255, 1992.

[ 75] S.W. Wallace and R. Wets. Preprocessing in stochastic programming: the case of linear

programs. ORSA J. on Computing, 4:45–59, 1992.

[ 74] R.T. Rockafellar and R. Wets. Scenarios and policy aggregation in optimization under

uncertainty. Mathematics of Operations Research, 16:119–147, 1991.

[ 73] J.R. Birge and R. Wets, editors. Stochastic Programming I & II. J.C. Baltzer AG, 1991.

[ 72] R. Wets. Scenario analysis vs. stochastic optimization. In G. Dantzig and P. Glynn,

editors, Resource Planning under Uncertainty for Electric Power Systems, pages 241–252.

Department of Operations Research, Stanford University, 1990.

[ 71] R.T. Rockafellar and R. Wets. Generalized linear-quadratic problems of deterministic and

stochastic optimal control in discrete time.

SIAM J. Control and Optimization, 28:810–822, 1990.

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

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

[ 69] J.R. Birge and R. Wets. Sublinear upper bounds for stochastic programs with recourse.

Mathematical Programming, 43:131–150, 1989.

[ 68] P. Varaiya and R. Wets. Stochastic dynamic optimization, approaches and computation.

In M. Iri and K. Tanabe, editors, Mathematical Programming, Recent Developments and

Applications, pages 309–332. Kluwer Academic Publisher, 1989.

[ 67] R. Wets. The aggregation principle in scenario analysis and stochastic optimization.

In S. Wallace, editor, Algorithms and Model Formulations in Mathematical Programming,

NATO ASI Vol.51, pages 91–113. Springer-Verlag, NATO ASI Vol.51,, 1989.

[ 66] T.K. Gates, R. Wets, and M.E. Grismer. Stochastic approximation applied to optimal

irrigation and drainage planning.

Journal of Irrigation and Drainage Engineering, 115:488–502, 1989.

[ 65] R. Wets. Stochastic programming. In G. Nemhauser, A. Rinnooy Kan, and M. Todd,

editors, Handbook for Operations Research and Management Sciences, Vol 1, pages 573–629.

Elsevier Science Publishers B.V. (North Holland), 1989.

[ 64] S.W. Wallace and R. Wets. Preprocessing in stochastic programming: the case of

uncapacitated networks. ORSA J. on Computing, 1:252–270, 1989.

[ 63] 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.

[ 62] A.J. King, R.T. Rockafellar, L. Somlýody, and R. Wets. Lake eutrophication management:

the lake Balaton project. In Y. Ermoliev and R. Wets, editors, Numerical Techniques for

Stochastic Optimization, pages 415–424. Springer, 1988.

[ 61] R. Wets. Large-scale linear programming techniques in stochastic programming.

In Y. Ermoliev and R. Wets, editors, Numerical Techniques for Stochastic Optimization,

pages 61–89. Springer, 1988.

[ 60] Y. Ermoliev and R. Wets. Numerical Techniques for Stochastic Optimization. Springer, 1988.

[ 59] J.L. Nazareth and R. Wets. Nonlinear programming techniques applied to stochastic

programs with recourse. In Y. Ermoliev and R. Wets, editors, Numerical Techniques for

Stochastic Optimization, pages 90–115. Springer, 1988.

[ 58] L. Somlýody and R. Wets. Stochastic optimization models for lake eutrophication

management. Operations Research, 36:660–681, 1988.

[ 57] R.T. Rockafellar and R. Wets. A note about projections in the implementation of stochastic

quasi-gradient methods. In Y. Ermoliev and R. Wets, editors, Numerical Techniques for

Stochastic Optimization Problems, pages 365–372. Springer, 1988.

[ 56] R. Wets. On parallel processors design for solving stochastic programs, II. In Proceedings

of International Conference on Numerical Optimization and Applications, pages 64–73.

Xi’an Jiaotong University, 1987.

[ 55] K.A. Ariyawansa, D.C. Sorensen, and R. Wets. Parallel schemes to approximate values

and subgradients of the recourse function in certain stochastic programs.

Argonne National Laboratories, 1987.

[ 54] S.M. Robinson and R. Wets. Stability in two-stage stochastic programming.

SIAM J. on Control and Optimization, 25:1409–1416, 1987.

[ 53] J.R. Birge and R. Wets. Computing bounds for stochastic programming problems by

means of a generalized moment problem. Mathematics of Operations Research,

12:149–162, 1987.

[ 52] 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.

[ 51] R.T. Rockafellar and R. Wets. A Lagrangian finite generation technique for solving

linear-quadratic problems in stochastic programming.

Mathematical Programming Study, 28:63–93, 1986.

[ 50] A. Prékopa and R. Wets, editors. Stochastic Programming 84 : I and II. North-Holland, 1986.

[ 49] V.I. Arkin, A. Shiraev, and R. Wets, editors. Stochastic Optimization. Proceedings of the

International Conference, Kiev, 1984,

vol. 81 of Lecture Notes in Control and Information Sciences. Springer, 1986.

[ 48] J.L. Nazareth and R. Wets. Algorithms for stochastic programs: the case of nonstochastic

tenders. Mathematical Programming Study, 28:1–28, 1986.

[ 47] R.T. Rockafellar and R. Wets. Linear-quadratic programming problems with stochastic

penalties: The finite generation algorithm. In V. Arkin, A. Shiraev, and R. Wets, editors,

Stochastic Optimization, Lecture Notes in Control and Information Sciences 81,

pages 543–560. Springer, 1986.

[ 46] J.R. Birge and R. Wets. Designing approximation schemes for stochastic optimization

problems, in particular stochastic programs with recourse.

Mathematical Programming Study, 27:54–102, 1986.

[ 45] R. Wets. Algorithmic procedures for stochastic optimization. In K. Schittkowski, editor,

Computational Mathematical Programming, pages 309–322. Springer, 1985.

[ 44] R. Wets. On parallel processors design for solving stochastic programs. In

Proceedings of the 6th Mathematical Programming Symposium Japan, pages 13–35.

Japan Mathematical Programming Society, 1985.

[ 43] J.R. Birge and R. Wets. Approximation and error bounds in stochastic programming.

In Y.L. Tong, editor, Inequalities in Statistics and Probability — Proceedings of the Symposium

on Inequalities in Statistics and Probability, Lincoln, Nebraska 1982, pages 178–186.

Institute of Mathematical Statistics, 1984.

[ 42] R. Wets. Modeling and solution strategies for unconstrained stochastic optimization

problems. Annals Operations Research, 1:3–22, 1984.

[ 41] R. Wets. Stochastic programming: solution techniques and approximation schemes.

In A. Bachem, M. Grö̈tschel, and B. Korte, editors,

Mathematical Programming: The State of the Art 1982, pages 566–603. Springer, 1983.

[ 40] R. Wets. Solving stochastic programs with simple recourse. Stochastics, 10:219–242, 1983. [ 39] R.T. Rockafellar and R. Wets. Deterministic and stochastic optimization problems of Bolza

type in discrete time. Stochastics, 10:273–312, 1983.

[ 38] R.T Rockafellar and R. Wets. A dual solution procedure for quadratic stochastic programs

with simple recourse. In V. Pereyra and A. Reinoza, editors, Numerical Methods,

Lecture Notes in Mathematics 1005, pages 252–265. Springer, 1983.

[ 37] R. Wets. Duality for stochastic Bolza problems with applications to a model for economic

growth and liquidity preference model. In G. Castellani and P. Mazzoleni, editors,

Mathematical Programming and Its Economic Applications, pages 405–419. F. Angeli, 1981.

[ 36] F. Solis and R. Wets. A statistical view of stochastic programming.

Manuscript, University of Kentucky, 1981.

[ 35] R. Wets. Stochastic multipliers, induced feasibility and nonanticipativity in stochastic

programming. In M. Dempster, editor, Stochastic Programming. Proceedings of the 1974

Oxford International Conference, pages 137–146. Academic Press, 1980.

[ 34] R. Wets. The distribution problem and its relation to other problems in stochastic

programming. In M. Dempster, editor, Stochastic Programming. Proceedings of the 1974

Oxford International Conference, pages 245–262. Academic Press, 1980.

[ 33] R. Wets. A statistical approach to the solution of stochastic programs with (convex)

simple recourse. Manuscript, University of Kentucky, 1979.

[ 32] R.T. Rockafellar and R. Wets. The optimal recourse problem in discrete time:

L1-multipliers for inequality constraints. f SIAM J. Control and Optimization, 16:16–36, 1978.

[ 31] R.T. Rockafellar and R. Wets. Measures as Lagrange multipliers in multistage stochastic

programming. J. Mathematical Analysis and Applications, 60:301–313, 1977.

[ 30] R.T. Rockafellar and R. Wets. Stochastic convex programming: relatively complete

recourse and induced feasibility. SIAM J. Control and Optimization, 14:574–589, 1976.

[ 29] R.T. Rockafellar and R. Wets. Stochastic convex programming: singular multipliers and

extended duality. Pacific J. of Mathematics, 62:507–522, 1976.

[ 28] R.T. Rockafellar and R. Wets. Nonanticipativity and L1-martingales in stochastic

optimization problems. Mathematical Programming Study, 6:170–187, 1976.

[ 27] R. Wets. Duality relations in stochastic programming. In Symposia Mathematica 19,

pages 341–355. Academic Press, 1976.

[ 26] R.T. Rockafellar and R. Wets. Stochastic convex programming: basic duality.

Pacific J. of Mathematics, 62:173–195, 1976.

[ 25] R. Wets. Solving stochastic programs with simple recourse II. In Proceedings Johns Hopkins

Symposium on System and Information Science, pages 1–6. Johns Hopkins University, 1975.

[ 24] R. Wets. On the relation between stochastic and deterministic optimization.

In A. Bensoussan and J.L. Lions, editors, Control Theory, Numerical Methods and Computer

Systems Modelling, Lecture Notes in Economics and Mathematical Systems, 107,

pages 350–361. Springer, 1975.

[ 23] R.T. Rockafellar and R. Wets. Stochastic convex programming: Kuhn-Tucker conditions.

J. of Mathematical Economics, 2:349–370, 1975.

[ 22] S. Garstka and R. Wets. On decision rules in stochastic programming.

Mathematical Programming, 7:117–143, 1974.

[ 21] R.T. Rockafellar and R. Wets. Continuous versus measurable recourse in N-stage

stochastic programming. J. Mathematical Analysis and Applications, 48:836–859, 1974.

[ 20] R. Wets. Stochastic programs with fixed recourse: the equivalent deterministic problem.

SIAM Review, 16:309–339, 1974.

[ 19] R. Wets. Induced constraints for stochastic optimization problems. In A. Balakrishnan,

editor, Techniques of Optimization, pages 433–443. Academic Press, 1972.

[ 18] R. Wets. Characterization theorems for stochastic programs.

Mathematical Programming, 2:166– 175, 1972.

[ 17] R. Wets. Stochastic programs with recourse: A basic theorem for multistage problems.

Z. Wahrswcheinlichkeitstheorie und verwandte Gebiete, 21:201–206, 1972.

[ 16] R. Wets. Some open questions in stochastic programming. In Proceedings of the Fourth

Conference on Probability Theory, pages 93–94. Editura Academica Republici Socialiste

Romania, 1971.

[ 15] R. Wets. Problèmes duaux en programmation stochastique.

Comptes Rendus de l’Académie des Sciences de Paris, 270:47–50, 1970.

[ 14] D. Walkup and R. Wets. Stochastic programs with recourse: special forms. In H. Kuhn,

editor, Proceedings of the Princeton Symposium on Mathematic Programming,

pages 139–162. Princeton University Press, 1970.

[ 13] D. Walkup and R. Wets. Stochastic programs with recourse II: On the continuity of the

objective. SIAM J. Applied Mathematics, 17:98–103, 1969.

[ 12] R. Van Slyke and R. Wets. L-shaped linear programs with application to optimal control

and stochastic programming. SIAM J. Applied Mathematics, 17:638–663, 1969.

[ 11] D. Walkup and R. Wets. A note on decision rules for stochastic programs.

J. on Computer Science, 2:305–311, 1968.

[ 10] R. Van Slyke and R. Wets. Stochastic programs in abstract spaces.

In H. Karreman, editor, Stochastic Optimization and Control, pages 24–45. J. Wiley, 1968.

[ 9] R. Van Slyke and R. Wets. A duality theory for abstract mathemtical programs with

applications to optimal control theory.

J. Mathematical Analysis and Applications, 22:679–706, 1968.

[ 8] R. Wets. A note on a paper by Charnes, Kirby and Raike.

Boeing Scientific Research Laboratories, 1968. Technical Report.

[ 7] R. Wets. Lectures on stochastic programming, University of California, Berkeley.

Lecture Notes, 1967.

[ 6] D. Walkup and R. Wets. Stochastic programs with recourse.

SIAM J. Applied Mathematics, 15:1299–1314, 1967.

[ 5] R. Wets. Programming under uncertainty: the solution set.

SIAM J. Applied Mathematics, 14:1143–1151, 1966.

[ 4] R. Wets. Programming under uncertainty: the equivalent convex program.

SIAM J. Applied Mathematics, 14:89–105, 1966.

[ 3] R. Van Slyke and R. Wets. Programming under uncertainty and stochastic optimal control.

SIAM J. Control, 4:179–193, 1966.

[ 2] R. Wets. Programming under uncertainty: the complete problem.

Z. Wahrswcheinlichkeitstheorie und verwandte Gebiete, 4:316–339, 1966.

[ 1] D. Kohler and R. Wets. Programming under uncertainty: an experimental code for the

’complete’ problem. Boeing Scientific Research Laboratories, 1964. Report #64-12.