Statistical approximation of multicriteria problems of stochastic programming
The article validates an approximation technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized, a vector “input–random output” system is considered. Random outputs are converted into a vector of deterministic performance/r...
Збережено в:
| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Видавничий дім "Академперіодика" НАН України
2015
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| Назва видання: | Доповіді НАН України |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/96220 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Statistical approximation of multicriteria problems of stochastic programming / B.V. Norkin // Доповiдi Нацiональної академiї наук України. — 2015. — № 4. — С. 35-41. — Бібліогр.: 12 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The article validates an approximation technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized, a vector “input–random output” system is considered. Random outputs are converted into a vector of
deterministic performance/risk indicators. The problem is to find those inputs that correspond
to Pareto-optimal values of output indicators. The problem is approximated by a sequence
of deterministic multicriteria optimization problems, where, for example, the objective vector
function is a sample average approximation of the original one, and the feasible set is a discrete sample approximation of the feasible inputs. Approximate optimal solutions are defined as weakly Pareto efficient ones within some vector tolerance. Convergence analysis includes
establishing the convergence of the general approximation scheme and establishing the conditions of convergence with probability one under proper regulation of sampling parameters. |
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