| Title |
Reikšmingų imčių metodas dviejų etapų stochastiniam tiesiniam uždaviniui / |
| Translation of Title |
Importance sampling method for two-stage linear stochastic problem. |
| Authors |
Dumskis, Valerijonas ; Sakalauskas, Leonidas |
| Full Text |
|
| Is Part of |
Jaunųjų mokslininkų darbai.. Vilnius : BMK leidykla. 2013, Nr. 2, p. 120-124.. ISSN 1648-8776 |
| Keywords [eng] |
two-stage linear stochastic problem ; Monte-Carlo method ; importance sampling ; convergence |
| Abstract [eng] |
In this paper, a two-stage linear stochastic problem is investigated, and solved by applying the method of approximation by sampling. When we approximate by samples, importance sampling is used, i.e., we choose samples for which values of variables lie in important regions. To solve the problem, we proposed a procedure in which the variance of sample and the ε - projection of stochastic gradient is used. This procedure converges almost certainly to the true solution of the problem. In this procedure, the size of the sample is regulated. The conditions for termination of the algorithm are also stated. The iterative process can be stopped by testing the statistical hypothesis of the equality of the gradient of the objective function to zero, when the confidence interval of the estimator of the objective function becomes of the proper accuracy. We then use importance sampling conditions for the stopping algorithm which are satisfied at the iterations whose number is less than using simple samples. The proposed method was investigated by solving the two-stage linear stochastic problem. Thus, the results obtained enable us to conclude that importance sampling enables us to decrease the number of iterations needed to achieve the termination conditions as well as to decrease the Monte-Carlo sample size at each iteration. |
| Published |
Vilnius : BMK leidykla |
| Type |
Journal article |
| Language |
Lithuanian |
| Publication date |
2013 |
