Abstract
This paper considers jointly chance constrained problems from the numerical point of view. The main numerical difficulties as well as techniques for overcoming these difficulties are discussed. The efficiency of the approach is illustrated by presenting computational results for large-scale jointly chance constrained test problems.
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References
Bukszár, J. (1999). Probability bounds with multitrees. Research Report RRR 5-99, RUTCOR.
Bukszár, J. and Prékopa, A. (1999). Probability bounds with cherry-trees. Research Report RRR 33-98, RUTCOR.
Deák, I. (1980). Three digit accurate multiple normal probabilities. Numerische Mathematik, 35:369–380.
Deák, I. (1990). Random number generators and simulation. Akadémiai Kiadó, Budapest.
Dupacovâ, J., Gaivoronski, A., Kos, Z., and Szântai, T. (1991). Stochastic programming in water management: A case study and a comparison of solution techniques. European Journal of Operational Research, 52:28–44.
Gassmann, H. I. (1988). Conditional probability and conditional expectation of a random vector. In Ermoliev, Y. and Wets, R.-B., editors, Numerical Techniques for Stochastic Optimization, pages 237–254. Springer Verlag.
Gröwe, N. (1997). Estimated stochastic programs with chance constraints. European Journal of Operational Research, 101:285–305.
Kail, P. (1976). Stochastic linear programming. Springer Verlag.
Kall, P. and Mayer, J. (1996). SLP-IOR: An interactive model management system for stochastic linear programs. Mathematical Programming, 75:221–240.
Kail, P. and Mayer, J. (1998a). On solving stochastic linear programming problems. In Marti, K. and Kail, P., editors, Stochastic Programming Methods and Technical Applications, pages 329–344. Springer Verlag.
Kall, P. and Mayer, J. (1998b). On testing SLP codes with SLP-IOR. In Giannessi, F., Rapcsák, T., and Komlósi, S., editors, New trends in mathematical programming, pages 115–135. Kluwer Academic Publishers.
Kail, P. and Wallace, S. W. (1994). Stochastic programming. John Wiley & Sons.
Mayer, J. (1992). Computational techniques for probabilistic constrained optimization problems. In Marti, K., editor, Stochastic Optimization: Numerical Methods and Technical Applications, pages 141–164. Springer.
Mayer, J. (1998). Stochastic Linear Programming Algorithms: A Comparison Based on a Model Management System. Gordon and Breach.
Murtagh, B. A. and Saunders, M. A. (1995). Minos 5.4 user’s guide. Technical Report SOL 83-20R, Department of Operations Research, Stanford University.
Norkin, V. I., Ermoliev, Y. M., and Ruszczynski, A. (1998). On optimal allocation of indivisibles under uncertainty. Operations Research, 46:381–395.
Prékopa, A. (1971). Logarithmic concave measures with applications to stochastic programming. Acta. Sci. Math, 32:301–316.
Prékopa, A. (1988). Numerical solution of probabilistic constrained programming problems. In Ermoliev, Y. and Wets, R.-B., editors, Numerical Techniques for Stochastic Optimization, pages 123–139. Springer Verlag.
Prékopa, A. (1995). Stochastic programming. Kluwer Academic Publishers.
Prékopa, A. (1999). The use of discrete moment bounds in probabilistic constrained stochastic programming models. Annals of Operations Research, 85:21–38.
Prékopa, A., Ganczer, S., Deák, I., and Patyi, K. (1980). The STABIL stochastic programming model and its experimental application to the electricity production in Hungary. In Dempster, M. A. H., editor, Stochastic Programming, pages 369–385. Academic Press.
Szántai, T. (1986). Evaluation of a special multivariate gamma distribution. Mathematical Programming Study, 27:1–16.
Szántai, T. (1987). Calculation of the multivariate probability distribution function values and their gradient vectors. Working Paper WP-87-82, IIASA.
Szántai, T. (1988). A computer code for solution of probabilistic-constrained stochastic programming problems. In Ermoliev, Y. and Wets, R.-B., editors, Numerical Techniques for Stochastic Optimization, pages 229–235. Springer Verlag.
Uryasev, S. and Rockafellar, R. T. (1999). Optimization of conditional Value-at-Risk. Research Report #99–4, Center for Applied Optimization, University of Florida.
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Mayer, J. (2000). On the Numerical Solution of Jointly Chance Constrained Problems. In: Uryasev, S.P. (eds) Probabilistic Constrained Optimization. Nonconvex Optimization and Its Applications, vol 49. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3150-7_12
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DOI: https://doi.org/10.1007/978-1-4757-3150-7_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4840-3
Online ISBN: 978-1-4757-3150-7
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