Abstract
In the paper, stability of the optimal solution of a stochastic program with recourse with respect to small changes of the underlying distribution of random coefficients is considered. As a tool, contamination of the given distribution by another one is suggested and the original stability problem is thus reduced to that with linearly perturbed objective function. The theory of perturbed Kuhn-Tucker points and strongly regular equations is used to get explicit formulas for Gâteaux differentials of optimal solutions under different assumptions. Possible exploitation of the results for further robustness studies is indicated.
Preview
Unable to display preview. Download preview PDF.
References
J. DupaČová, ”Minimaxová úloha stochastického, lineárního programování a momentový problém“, Ekonomicko-matematický obzor 13 (1977) 279–307. (Extended abstract: ”Minimax approach to stochastic linear programming and the moment problem. Selected results“ Zeitschrift für Angewandte Mathematik und Mechanik 58 (1978) T466–T467.)
J. DupaČová, ”On minimax decision rule in stochastic linear programming“, in: A. Prékopa, ed., Mathematical methods of operations research 1 (Akademiai Kiaidó, Budapest, 1980) pp. 38–48.
J. DupaČová, ”Stability studies in stochastic programs with recourse. The special case“, Zeitschrift für Angewandte Mathematik und Mechanik 62 (1982) T369–T370.
J. DupaČová, ”Stability in stochastic programming with recourse“, Acta Universitatis Carolinae-Mathematica et Physica 24 (1983) 23–34.
J. DupaČová, ”Stability in stochastic programming with recourse-Estimated parameters“, Mathematical Programming 28 (1984) 72–83.
J. DupaČová, ”The minimax approach to stochastic programming and an illustrative application“, to appear in Stochastics.
A.V. Fiacco, ”Sensitivity analysis for nonlinear programming using penalty methods“, Mathematical Programming 10 (1976) 287–311.
H. Gfrerer, J. Guddat and Hj. Wacker, ”A globally convergent algorithm based on imbedding and parametric optimization“, Computing 30 (1983) 225–252.
F.R. Hampel, ”The influence curve and its role in robust estimation“, Journal of the American Statistical Association 69 (1974) 383–397.
P. Kall and D. Stoyan, ”Solving stochastic programming problems with recourse including error bounds“, Mathematische Operations forschung und Statistik, Ser. Optimization 13 (1982) 431–447.
R. Nadeau and R. Theodorescu, ”Restricted Bayes strategies for programs with simple recourse“, Operations Research 28 (1980) 777–784.
S.M. Robinson, ”Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms“, Mathematical Programming 7 (1984) 1–16.
S.M. Robinson, ”Strongly regular generalized equations“, Mathematics of Operations Research 5 (1980) 43–62.
H. Schneeweiss, Entscheidungskriterien bei Risiko (Springer-Verlag, Berlin, 1967).
J. Wang, ”Distribution sensitivity analysis for stochastic programs with recourse“, to appear in Mathematical Programming.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 The Mathematical Programming Society, Inc.
About this chapter
Cite this chapter
DupaČová, J. (1986). Stability in stochastic programming with recourse. Contaminated distributions. In: Prékopa, A., Wets, R.J.B. (eds) Stochastic Programming 84 Part I. Mathematical Programming Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121117
Download citation
DOI: https://doi.org/10.1007/BFb0121117
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00924-2
Online ISBN: 978-3-642-00925-9
eBook Packages: Springer Book Archive