Stochastic Optimization: Algorithms and Applications by Jitka Dupačová (auth.), Stanislav Uryasev, Panos M. Pardalos

By Jitka Dupačová (auth.), Stanislav Uryasev, Panos M. Pardalos (eds.)

Stochastic programming is the examine of methods for choice making less than the presence of uncertainties and dangers. Stochastic programming ways were effectively utilized in a couple of components comparable to power and creation making plans, telecommunications, and transportation. lately, the sensible event received in stochastic programming has been extended to a far greater spectrum of purposes together with monetary modeling, hazard administration, and probabilistic threat research. significant themes during this quantity comprise: (1) advances in conception and implementation of stochastic programming algorithms; (2) sensitivity research of stochastic structures; (3) stochastic programming purposes and different comparable topics.
Audience: Researchers and academies operating in optimization, laptop modeling, operations learn and fiscal engineering. The publication is acceptable as supplementary interpreting in classes on optimization and monetary engineering.

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75, 277-293. [25] Gaivoronski, A. A. (1991), "A numerical method for solving stochastic programming problems with moment constraints on a distribution function," Annals of Oper. , 31, 347-369. 26 J. DUPACOVA. [26] Gol'shtein, E. G. (1970), Vypukloje Programmirovanie. Elementy Teoriji, Nauka, Moscow. [Theory of Convex Programming, Translations of Mathematical Monographs, 36, American Mathematical Society, Providence RI, 1972]. , Kiwiel, K. , Nowak, M. , Romisch, W. and Wegner, 1. de/speps/. [28] Kall, P.

EFRAIMIDIS and P. SPIRAKIS Proof: 1. PROB{C2UC3}::; PROB{C2} + PROB{C3}::; p . 2. 1 Algorithm A-SUM is a O(n)-time RFPTAS for SUM with probability of success at least 1 - p, where p a fixed real in (0,1). 6 Conclusions We showed that combining standard randomized rounding with combinatorial techniques can considerably improve the performance of randomized rounding technique. The enhancement due to the combinatorial techniques is two-fold. First the LP relaxation is made very tight and second the randomized rounding procedure is checked for "unlucky" choices which are corrected.

The size of the deviations depends on the tightness of the LP relaxation or else the gap between the optimal solutions for the original integer program and the corresponding relaxed linear program and on the efficiency of the rounding procedure. We show that in specific settings combinatorial techniques significantly improve the approximation guarantee of the randomized rounding procedure. The combinatorial techniques act on the randomized rounding procedure 1. by reducing the gap between the integer program and its linear programming relaxation, and 2.

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