Implementation of parallel optimization algorithms using generalized branch and bound template. (English) Zbl 1113.90170

Bogle, I. D. L. (ed.) et al., Computer aided methods in optimal design and operations. Papers based on the presentations at the workshop, Vilnius, Lithuania, February 15–17, 2006. Hackensack, NJ: World Scientific (ISBN 981-256-909-X/hbk). Series on Computers and Operations Research 7, 21-28 (2006).
Summary: We consider problems related to the implementation of Stochastic Approximation (SA) in technical design, namely, estimation of a stochastic gradient, improvement of convergence, stopping criteria of the algorithm, etc. The accuracy of solution and the termination of the algorithm are considered in a statistical way. We build a method for estimation of confidence interval of the objective function extremum and stopping of the algorithm according to order statistics of objective function values provided during optimization. We give some illustration examples of application of the developed approach of SA to the optimal engineering design problems, too.
For the entire collection see [Zbl 1103.90009].


90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
68W10 Parallel algorithms in computer science
90C15 Stochastic programming