Study on the Evolution, Results and Trends of Applying Stochastic Optimization

Hampu, Alexandru; Căruţaşu, Vasile

doi:10.2478/kbo-2019-0112

Abstract

This paper aims to analyze the stage reached in the development and application of stochastic optimization models, highlighting some of the most important moments and achievements in the field. The author tries to identify particular aspects that define the classes of stochastic optimization models, specifying the level reached in certain directions of research and implementation of these models in order to identify possible directions of development of these specific techniques.

References

[1] Beale, E.M.L., On Minimizing a Convex Function Subject to Linear Inequalities, Journal of the Royal Statistical Society. Series B, vol 17 (2), pp.173-184, 1955.10.1111/j.2517-6161.1955.tb00191.x
Search in Google Scholar Back to article
[2] Bereanu, B., On Stochastic Linear Programming. Distributions Problems, Stochastic Technology Matrix, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 8, pp.148-152, 1967.10.1007/BF00536917
Search in Google Scholar Back to article
[3] Bereanu, B., The Continuity of the Optimumin Parametric Programming and Applications to Stochastic Programming, J. of Opt. Theory and its Applications 18, pp.319-333, 1976.10.1007/BF00933815
Search in Google Scholar Back to article
[4] Bereanu, B., The Distribution Problem in Stochastic Linear Programming. The Cartesian Integration Method, Reprint No. 7103, Center of Mathematical Statistics of the Academy of the Socialist Republic of Romania, Bucharest, pp.71-103, 1971.
Search in Google Scholar Back to article
[5] Bereanu, B., Some Numerical Methods in Stochastic Linear Programming under Risk and Uncertainty, Stoch. Programming (M.A.H. Dempster, ed), Academic Press, London, pp.196-205, 1980.
Search in Google Scholar Back to article
[6] Charnes, A., Cooper, W.W. și Symonds, G.H. Cost Horizons and Certainty Equivalents: an Approach to Stochastic Programming of Heating Oil, Management Sci., 4, pp.235-263, 195810.1287/mnsc.4.3.235
Search in Google Scholar Back to article
[7] Charnes, A., Cooper, W.W., Deterministic Equivalents for Optimizating and Satisfying under Chance Constraint., Operation Research 11(1), pp.18-39, 1963.10.1287/opre.11.1.18
Search in Google Scholar Back to article
[8] Dantzig, G.B., Linear Programming under Uncertainty, Management Sci., 1, pp.197-206, 1955.10.1287/mnsc.1.3-4.197
Search in Google Scholar Back to article
[9] Dantzig, G.B. and Wolfe,P., The DescompositionAlgorithm for Linear Programs, Econometrica, vol.29, pp.767-778, 1961.10.2307/1911818
Search in Google Scholar Back to article
[10] Ewbank, J.B., Foote, B.L., Kumin. H.J., A Method for the Solution of the Distribution Problem of Stochastic Linear Programming, SIAM J. Appl. Math., 26, pp.237-243, 1974.10.1137/0126020
Search in Google Scholar Back to article
[11] Lageweg, B.J., Lenstra, J.K.,Rinnoy Kan, A.H.G.R., Stougie, L., Stochastic Integer Programming by Dynamic Programming, StatisticaNeerlandica, 39 (2), 97-113, 1985.10.1111/j.1467-9574.1985.tb01131.x
Search in Google Scholar Back to article
[12] Lemke, C.E., The Dual Method for Solving the Linear Programming Problem, Naval Research Logistic Quarterly 1, pp.36-47, 1954.10.1002/nav.3800010107
Search in Google Scholar Back to article
[13] Prékopa, A., Stochastic Programming, AkadémiaKiadó, Budapest, 1995.10.1007/978-94-017-3087-7
Search in Google Scholar Back to article
[14] Prékopa, A., Dual Method for a One-stage Stochastic Programming Problem with Random RHS Obeying a Discrete Probability Distribution, Zeitschrift fur Op.Research, 38, pp.441-461, 1990.10.1007/BF01421551
Search in Google Scholar Back to article
[15] Sen, S. and Liu, Y., Mitigating Uncertainty via Compromise Decision in Two-stage Stochastic Linear Programming,Operations Research 64 (6), 1422-1437, 2014.10.1287/opre.2016.1526
Search in Google Scholar Back to article
[16] Slyke, R,. van, Wets, R.J.-B., L-shaped Linear Program with Applica.tion to Optimal Control and Stochastic Linear Programs, SIAM J. on Applied Math. 17, pp.638-663, 196910.1137/0117061
Search in Google Scholar Back to article
[17] Stancu-Minasian, I.M., Programareastochastică cu mail multefuncțiiobiectiv, Ed. AcademieiRSR, 1980.
Search in Google Scholar Back to article
[18] Stougie, L., Design and Analysis of Algorithms for Stochastic Integer Programming, CWI Tract 37, Centrum voorWiskundeen Informatica, Amsterdam, 1987.
Search in Google Scholar Back to article
[19] Strazicky, B., Computational Experience with Algorithm for Discrete Recourse Problems, Stochastic Programming (M.A.H. Dempster, ed.) Academis Press, London, pp.263-274, 1980.
Search in Google Scholar Back to article
[20] Tintner, G., Stochastic Linear Programming with Applications to Agricultural Economicsz, Proseedings of the Second Symposium in Linear Programming, H.A. Antotosiewicz (ed.) National Bureau Standard, Washington, pp. 197-228, 1955.
Search in Google Scholar Back to article
[21] Wets, R.J.-B., Programming under uncertainty: the complete problem, Z. WahrscheinlichkeitstheorieVerw, Gebiete, 4, pp.316-339, 1966.10.1007/BF00539117
Search in Google Scholar Back to article
[22] Wets, R.J.-B., Solving stochastic programs with simple recourse, Stochastics 10, pp.219-242, 1983.10.1080/17442508308833274
Search in Google Scholar Back to article
[23] Wollmer, R.M., Two-stage linear programming under uncertainty with 0-1 first stage variables, Mathematical programming 19, pp.279-288, 1980. https://www.aimms.com. https://www.solver.com/xpress-solver-engine10.1007/BF01581648
Search in Google Scholar Back to article

Study on the Evolution, Results and Trends of Applying Stochastic Optimization

Abstract

Paradigm

My account