Acta Oeconomica Pragensia 2007, 15(4):111-120 | DOI: 10.18267/j.aop.80

Role of Dependence in Chance-constrained and Robust Programming

Michal Houda
Mgr. Michal Houda - student of doctoral study; Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, 121 16 Prague 2, houda@karlin.mff.cuni.cz

The paper deals with two methods of solving optimization programs where uncertainties occur: stochastic (in particular chance-constrained) programming and robust programming. We review briefly how these two methods deal with uncertainty and what approximations are commonly used. Furthermore, we are concentrated on approximations based on sample sets where some type of weak dependence occurs. We demonstrate that such kind of dependence does not imply any important malfunction of optimization methods used there. Numerical illustration on simple optimization program is given.

Keywords: stochastic programming, robust programming, weak dependence
JEL classification: C44, C61

Published: August 1, 2007  Show citation

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Houda, M. (2007). Role of Dependence in Chance-constrained and Robust Programming. Acta Oeconomica Pragensia, 15(4), 111-120. doi: 10.18267/j.aop.80
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    References

    1. BEN-TAL, A.; NEMIROVSKI, A. (1998). Robust convex optimization. Mathematics of Operations Research, 1998, vol. 23, no. 4, pp. 769-805. Go to original source...
    2. BIRGE, J. R.; LOUVEAUX, F. (1997). Introduction To Stochastic Programming. New York, Springer-Verlag, 1997.
    3. CALAFIORE, G.; CAMPI, M. C. (2005). Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming, 2005, vol. 102, no. 1 (ser. A), pp. 25-46. Go to original source...
    4. DANTZIG, G. B. (1947). Programming in a linear structure. Econometrica, 1949, vol. 17, pp. 73-74. Go to original source...
    5. DANTZIG, G. B. (1955). Linear programming under uncertainty. Management Science, 1955, vol. 1, pp. 197-206. Go to original source...
    6. DENTCHEVA, D.; LAI, B.; RUSZCZYŇSKI, A (2004). Dual methods for probabilistic optimization problems. Mathematical methods of operations research, 2004, vol. 60, no. 2, pp. 331-346. Go to original source...
    7. de FARIAS, D. P.; VAN ROY, B. (2004). On constraint sampling in the linear programming approach to approximate dynamic programming. Mathematics of Operations Research, 2004, vol. 29, no. 3, pp. 462-478. Go to original source...
    8. El GHAOUI, L.; OUSTRY, F.; LEBRET, H. (1998). Robust solutions to uncertain semidefinite programs. SIAM Journal of Optimization, 1998, vol. 9, no. 1, pp. 33-52. Go to original source...
    9. GOLDFARB, D.; IYENGAR, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 2003, vol. 28, no. 1, pp. 1-38. Go to original source...
    10. HOUDA, M. (2006a). Comparison of approximations in stochastic and robust optimization programs. In Hušková, M.; Janžura, M. (eds.) Prague Stochastics 2006. Prague, Matfyzpress, 2006, pp. 418-425.
    11. HOUDA, M. (2006b). Approximations in stochastic and robust programming problems. In Lukáš, L. (ed.). Proceedings of the 24th International Conference Mathematical Methods in Economics 2006. Plzeň, University of West Bohemia in Pilsen, 2006, pp. 249-254.
    12. KALL, P.; WALLACE, S. W. (1994). Stochastic Programming. Chichester : Wiley, 1994.
    13. PRÉKOPA, A. (1995). Stochastic Programming. Budapest : Akadémiai Kiadó, 1995. Go to original source...
    14. ROMISCH, W. (2003). Stability of stochastic programming problems. In Ruszczynski, A.; Shapiro, A. (eds.) Stochastic Programming. Handbooks in Operations Research and Management Science, Vol. 10. Amsterdam : Elsevier, 2003,pp. 483-554. Go to original source...
    15. RUSZCZYŇSKI, A.; SHAPIRO, A. (eds.) (2003). Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, Amsterdam : Elsevier, 2003. Go to original source...
    16. YOSHIHARA, K. (1992). Summation theory for weakly dependent sequences. Weakly dependent stochastic sequences and their applications (Vol. 1). Tokyo : Sanseido, 1992.

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