### Leonidas Sakalauskas (Institute of Mathematics and Informatics, Vilnius, Lithuania)

#### Parallel adaptation of Monte-Carlo method for continuous stochastic
programming

*Wednesday 9 December 2009 at 15.30, JCMB 6206*

##### Abstract

The objective of the research is the development of parallel algorithms
for solving stochastic programming problems by finite sequences of
Monte-Carlo estimators. The algorithms are based by adaptive regulation of
the Monte-Carlo sample size and the statistical termination procedure. The
approach distinguishes itself by treatment of the accuracy of the solution
in a statistical manner, testing the hypothesis of optimality according to
statistical criteria, and estimating confidence intervals of the objective
and constraint functions. The adjustment of sample size taking it
inversely proportional to the square norm of Monte-Carlo estimator of
gradient guarantees the convergence of the method and enables us to solve
the problem by reasonable amount of computations. To avoid "jamming"
or "zigzagging" in solving the problem, the εâ€“feasible direction
approach is implemented. The method developed was applied to solve
examples from the database of two-stage stochastic linear programming
tests. Many solutions given in the database were achieved by the method
developed and in a number of cases we had success to improve the solution
given in database. High performance computers with parallel computing
allowed us to perform computational statistical experiment, which has high
practical importance pursuing to explore the speedup and efficiency of
parallelization on the number of processors and admissible accuracy. The
parallelization strategy consists of sharing the computation of identical
Monte-Carlo trials among processors and using root processor to manage the
adaptation of the sample size. Portable parallel programs were developed
with MPICC which can be used on any parallel architecture.

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