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Read or Download Contributions to Operations Research: Proceedings of the Conference on Operations Research Held in Oberwolfach, West Germany February 26 – March 3, 1984 PDF

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Additional info for Contributions to Operations Research: Proceedings of the Conference on Operations Research Held in Oberwolfach, West Germany February 26 – March 3, 1984

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Elster; R. Nehse: Generalizations of conjugate functions. In: Pr'kopa, A. ): Survey of Mathematical Programming (Proceedings of 9th Internat. Mathem. Programming SympOSium, Budapest 1976). Akademiai Kiad6, Budapest 1919, Vol. 1 ) 193 - 204. : On the theory of nonconvex optimization problems. In: W. Oettli and F. Steffens (eda): Proceedings III. Symp. , Mennheim (BRD) 1918; Operations Research Verfahren, Vol. 31, 173-184. ; R. Deumlich: On duality concepts for nonconvex optimization problems. In: R.

H. BIster: Duality theorems and optimality conditions for nonconvex optimization problems. Math. Operationsforsch. u. , Sere optimization, 11 (1980), 2, 181 - 219. -H. Elster: On the theory of conjugate functions. In: Studies on Mathematical Programming. Akad~miai Kiad6, Budapest 1980, 19 - 45. -H. Elsterl Reoent results on f-conjugation and nonconvex optimization. Inl G. Feichtinger and P. RaIl (ed&), Operations Research in Progress. D. Reidel Publ. Comp. 1982, 27 - 40. -H. Elster: Theorie nichtkonvexer Optimierungsprobleme: Stabilit~t und Dualitat.

3) P(Ys>t) = P(sup nE :N S~(t»ds(t» $ exp(-u(t) ·ds(t». 3) we get Lemma 1: Let u: (EX1;M) ~ (o;~) be defined by Ee u(t)X 1 etu(t) • Then u is measurable and with ys:= max(EX 1 ,S/N) VN(s) lOV~(S):= Ys + f (Ys;M) exp[-u(t)·(Nt-s»)dt Remark: V~(s) ~Ys = V~(S) ~~. 1)' converge to v*. 5. Improved bounds for the Sn/n problem We now apply the results of section 4 to the Sn/n stopping problem of the introduction. Here P(X 1=1) = P(X 1 = -1) = 1/2, hence M=1, EX 1 =0 and ys=s +/N. Lemma 1 reduces to Corollary 2: Let u: (0;1) be defined by ~ (O;~) cosh u(t) = etu(t) for each t.

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