Zusammenfassung
Betrachtet wird eine Folge zufallsabhängiger Optimierungsprobleme, die sich z.B. bei der Approximation unbekannter Größen eines vorgegebenen deterministischen Optimierungsproblems durch Schätzungen ergibt. Ausgehend von geeigneten Konvergenzbegriffen für zufällige Folgen und zufällige Funktionen werden Aussagen über das Verhalten der Optimalwerte und der Lösungsmengen bereitgestellt.
Abstract
The paper deals with a sequence of random optimization problems which may arise when unknown quantities of a given deterministic optimization problem are replaced by estimates. Making use of suitable convergence notions for random sets and random functions assertions on the behaviour of the optimal values and the solution sets are derived.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature
Bank, B.; Guddat, J.; Klatte, D.; Kummer, B.; Tammer, K. Non-linear parametric optimization. Berlin: Akademie-Verlag (1982)
Castaing, C; Valadier, M. Convex analysis and measurable multifunctions. Lecture Notes in Mathematics 580, Springer-Verlag (1977)
Dupačová, J. Stability and sensitivity analysis for stochastic programming. Annals of Operations Research (to appear)
Kall, P. On approximations and stability in stochastic programming. In: Parametric optimization and related topics (J. Guddat et al., (eds.), Berlin: Akademie-Verlag (1987), 387–407
King, A.J.; Wets, R.J.-B. Epi-consistency of convex stochastic programs. Stochastics and Stochastics Reports (to appear)
Michel, R.; Pfanzagl, J. The accuracy of the normal approximation for minimum contrast estimates. Z. Wahrscheinlichkeitstheorie verw. Geb. 18 (1971), 73–84
Robinson, S.M. Local epi-continuity and local optimization. Mathematical programming 37 (1987), 208–222
Robinson, S.M.; Wets, R.J.-B. Stability in two-stage stochastic programming. SIAM Journal on Control and Optimiz. 25 (1987), 1409–1416
Römisch, W. On the convergence of measurable selections and an application to approximations in stochastic optimization. Zeitschrift für Analysis und ihre Anwendungen 5 (1986), 277–288
Römisch, W.; Schultz, R. Distribution sensitivity in stochastic programming. Mathematical Programming (to appear)
Salinetti, G.; Wets, R.J.-B. On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. Mathematics of Operations Research 11 (1986), 385–419
Vogel, S. Stability results for stochastic programming problems. Optimization 19 (1988), 269–288
Vogel, S. Stochastische Stabilitätskonzepte. Manuscript, Technische Hochschule Ilmenau (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Vogel, S. (1992). Stochastic Stability Concepts. In: Bühler, W., Feichtinger, G., Hartl, R.F., Radermacher, F.J., Stähly, P. (eds) Papers of the 19th Annual Meeting / Vorträge der 19. Jahrestagung. Operations Research Proceedings, vol 1990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77254-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-77254-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55081-5
Online ISBN: 978-3-642-77254-2
eBook Packages: Springer Book Archive