Statistical approximation of multicriteria problems of stochastic programming

TitleStatistical approximation of multicriteria problems of stochastic programming
Publication TypeJournal Article
Year of Publication2015
AuthorsNorkin, BV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.04.035
Issue4
SectionInformation Science and Cybernetics
Pagination35-41
Date Published4/2015
LanguageEnglish
Abstract

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.

Keywordsapproximation, multicriteria, stochastic programming
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