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Engl, Heinz W.

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

Appl. Math. Optimization 5, 271-281 (1979).
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Cited in 2 Reviews
Cited in 3 Documents

MSC:

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

Keywords:

existence of measurable optima; measurability; parametric programming; stochastic linear programming; nonlinear stochastic optimization; stochastic control

Citations:

Zbl 0352.90044
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\textit{H. W. Engl}, Appl. Math. Optim. 5, 271--281 (1979; Zbl 0418.90067)
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References:

[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).
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