Abstract
Application of the regularized decomposition method to large scale structured linear programming problems arising in stochastic programming is discussed. The method uses a quadratic regularizing term to stabilize the master but is still finitely convergent. Its practical performance is illustrated with numerical results for large real world problems.
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References
Birge J.R. and F.V. Louveaux, “A multicut algorithm for two-stage stochastic linear programs,” European Journal of Operations Research 34(1988) 384–392.
Birge J.R. and R.J.-B. Wets, “Designing approximation schemes for stochastic approximation problems, in particular for stochastic programs with recourse,” in: Stochastic Programming 1984, A. Prekopa and R.J.-B. Wets (eds.), Mathematical Programming Study 27(1986) 54–102.
Dantzig G. and A. Madansky, “On the solution of two-stage linear programs under uncertainty,” in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley 1961, pp. 165–176.
Dantzig G. and P. Wolfe, “Decomposition principle for linear programs,” Operations Research 8(1960) 101–111.
Ermoliev Yu. and R.J.-B. Wets (eds.), Numerical Techniques for Stochastic Optimization, Springer Verlag, Berlin 1988.
Kall P., A. Ruszczyñski and K. Frauendorfer, “Approximation techniques in stochastic programming,” in: Numerical Techniques for Stochastic Optimization (Yu. Ermoliev and R. Wets, eds.), Springer-Verlag, Berlin 1988, pp. 33–64.
Kiwiel K.C., Methods of Descent for Nondifferentiable Optimization, Springer-Verlag, Berlin, 1985.
Marsten R., “The design of the XMP linear programming library,” ACM Transactions of Mathematical Software 7(1981) 481–497.
Mulvey J.M. and A. Ruszczyński, “A new scenario decomposition method for large-scale stochastic optimization,” technical report SOR-91–19, Dea-partment of Civil Engineering and Operations Research, Princeton University, Princeton 1991 (to appear in Operations Research).
Ruszczyński A., “A regularized decomposition method for minimizing a sum of polyhedral functions,” Mathematical Programming 35(1986) 309–333.
Ruszczyński A., “An augmented Lagrangian decomposition method for block diagonal linear programming problems,” Operations Research Letters 8(1989) 287–294.
Ruszczyński A., “Parallel decomposition of multistage stochastic programming problems,” Mathematical Programming 58(1993) 201–228.
Ruszczyński A., “Regularized decomposition of stochastic programs: algorithmic techniques and numerical results,” working paper WP-93–21, International Institute for Applied Systems Analysis, Laxenburg 1993.
Sen S., R.D. Doverspike and S. Cosares, “Network planning with random demand,” technical report, Department of Systems and Industrial Engineering, University of Arizona, Tucson, 1992.
Topkis J.M., “A cutting plane algorithm with linear and geometric rates of convergence,” Journal of Optimization Theory and Applications 36(1982) 1–22.
Van Slyke R. and R.J.-B. Wets, “L-shaped linear programs with applications to optimal control and stochastic programming,” SIAM Journal on Applied Mathematics 17(1969) 638–663.
Wets R.J.-B., “Stochastic programs with fixed recourse: the equivalent deterministic program,” SIAM Review 16(1974) 309–339.
Wets R.J.-B., “Large scale linear programming techniques,” in: Numerical Techniques for Stochastic Optimization (Yu. Ermoliev and R. Wets, eds.), Springer-Verlag, Berlin 1988, pp. 65–94.
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© 1995 Springer-Verlag Berlin Heidelberg
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Ruszczyński, A. (1995). On the Regularized Decomposition Method for Stochastic Programming Problems. In: Marti, K., Kall, P. (eds) Stochastic Programming. Lecture Notes in Economics and Mathematical Systems, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88272-2_6
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DOI: https://doi.org/10.1007/978-3-642-88272-2_6
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