Existence of measurable optima in stochastic nonlinear programming and control. (English) Zbl 0418.90067


90C15 Stochastic programming
90C30 Nonlinear programming
90C31 Sensitivity, stability, parametric optimization
49J55 Existence of optimal solutions to problems involving randomness
93E20 Optimal stochastic control


Zbl 0352.90044
Full Text: DOI


[1] A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis,Bull. of the Amer. Math. Soc., 82, 641-657 (1976). · Zbl 0339.60061
[2] H. W. Engl, E. A. Zarzer and Hj. Wacker, Ausgewählte Aspekte der Kontrolltheorie; in: H. Noltemeier (ed.),Computergestützte Planungssysteme, Physica-Verlag, Würzburg-Wien, 155-202 (1976). · Zbl 0388.49003
[3] H. W. Engl, Some random fixed point theorems for strict contractions and nonexpansive mappings,Nonlinear Analysis, 2, 619-626 (1978). · Zbl 0382.60068
[4] H. W. Engl, A general stochastic fixed point theorem for continuous random operators on stochastic domains,Jour. Math. Anal. Appl., 66, 220-231 (1978). · Zbl 0398.60063
[5] H. W. Engl, Random fixed point theorems for multivalued mappings,Pacific J. Math., 76, 351-360 (1978). · Zbl 0355.47035
[6] H. W. Engl, Random fixed point theorems, in: V. Lakshmikantham (ed.),Nonlinear Equations in Abstract Spaces, Academic Press, New York, pp. 67-80 (1978).
[7] O. Han?, Random fixed point theorems; in: Trans. First Prague Conf. on Information Theory, Statist. Decision Functions and Random Processes (Liblice, 1956), Czechoslovak. Acad. Sci., Prague, 105-125 (1957).
[8] W.-R. Heilmann, Optimal selectors for stochastic linear programs,Appl. Math. Opt., 4, 139-142 (1978). · Zbl 0371.90106
[9] C. J. Himmelberg, Measurable relations,Fundamenta Math., 87, 53-72 (1975). · Zbl 0296.28003
[10] S. Itoh, A random fixed point theorem for a multivalued contraction mapping,Pacific J. Math., 68, 85-90 (1977). · Zbl 0335.54036
[11] P. Kall,Stochastic Linear Programming, Springer-Verlag, Berlin (1976). · Zbl 0317.90042
[12] K. Kuratowski-C. Ryll-Nardzewski, A general theorem on selectors,Bull. Acad. Polon. Sc. (Sér. math., astr. et phys.), 13, 397-403 (1965).
[13] A. Nowak, Random fixed points of multifunctions, Prace Naukowe Uniwersytetu Slaskiego: Prace Matematyczne, Katowice, Poland, (to appear). · Zbl 0504.60070
[14] M. Schäl, A selection theorem for optimization problems,Arch. Math., 25, 219-224 (1974). · Zbl 0351.90069
[15] K. Tammer, On the solution of the distribution problem of stochastic programming, Colloquia Mathematica Soc. János Bolyai, 12.Progress in Operations Research, Eger (Hungary), 907-920 (1974).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.