Two-stage stochastic linear programming by a series of Monte-Carlo estimators
<p class="Abstract">In this paper a stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte-Carlo sampling estimators. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical terminati...
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| Format: | Article |
| Language: | English |
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Klaipėda University
2015-07-01
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| Series: | Computational Science and Techniques |
| Online Access: | http://journals.ku.lt/index.php/CST/article/view/891 |
| _version_ | 1830308331007246336 |
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| author | Kęstutis Žilinskas |
| author_facet | Kęstutis Žilinskas |
| author_sort | Kęstutis Žilinskas |
| collection | DOAJ |
| description | <p class="Abstract">In this paper a stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte-Carlo sampling estimators. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical termination procedure taking into consideration statistical modelling accuracy. Our approach distinguishes itself by the treatment of 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. To avoid “jamming” or “zigzagging” solving a constraint problem we implement the ε–feasible direction approach. The proposed adjustment of a sample size, when it is taken inversely proportional to the square of the norm of the Monte-Carlo estimate of the gradient, guarantees convergence a. s. at a linear rate. The numerical study and examples in practice corroborate theoretical conclusions and show that the developed procedures make it possible to solve stochastic problems with sufficient accuracy by the means of an acceptable size of computations.</p><p class="Abstract">DOI: 10.15181/csat.v2i2.891</p> |
| first_indexed | 2024-12-19T10:47:24Z |
| format | Article |
| id | doaj.art-55476ceda6064346bfe3e8670ea3026a |
| institution | Directory Open Access Journal |
| issn | 2029-9966 |
| language | English |
| last_indexed | 2024-12-19T10:47:24Z |
| publishDate | 2015-07-01 |
| publisher | Klaipėda University |
| record_format | Article |
| series | Computational Science and Techniques |
| spelling | doaj.art-55476ceda6064346bfe3e8670ea3026a2022-12-21T20:25:12ZengKlaipėda UniversityComputational Science and Techniques2029-99662015-07-012228931210.15181/csat.v2i2.891931Two-stage stochastic linear programming by a series of Monte-Carlo estimatorsKęstutis Žilinskas0Šiauliai University<p class="Abstract">In this paper a stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte-Carlo sampling estimators. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical termination procedure taking into consideration statistical modelling accuracy. Our approach distinguishes itself by the treatment of 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. To avoid “jamming” or “zigzagging” solving a constraint problem we implement the ε–feasible direction approach. The proposed adjustment of a sample size, when it is taken inversely proportional to the square of the norm of the Monte-Carlo estimate of the gradient, guarantees convergence a. s. at a linear rate. The numerical study and examples in practice corroborate theoretical conclusions and show that the developed procedures make it possible to solve stochastic problems with sufficient accuracy by the means of an acceptable size of computations.</p><p class="Abstract">DOI: 10.15181/csat.v2i2.891</p>http://journals.ku.lt/index.php/CST/article/view/891 |
| spellingShingle | Kęstutis Žilinskas Two-stage stochastic linear programming by a series of Monte-Carlo estimators Computational Science and Techniques |
| title | Two-stage stochastic linear programming by a series of Monte-Carlo estimators |
| title_full | Two-stage stochastic linear programming by a series of Monte-Carlo estimators |
| title_fullStr | Two-stage stochastic linear programming by a series of Monte-Carlo estimators |
| title_full_unstemmed | Two-stage stochastic linear programming by a series of Monte-Carlo estimators |
| title_short | Two-stage stochastic linear programming by a series of Monte-Carlo estimators |
| title_sort | two stage stochastic linear programming by a series of monte carlo estimators |
| url | http://journals.ku.lt/index.php/CST/article/view/891 |
| work_keys_str_mv | AT kestutiszilinskas twostagestochasticlinearprogrammingbyaseriesofmontecarloestimators |