Random approximations in multiobjective optimization

作     者：Vogel, Silvia 

作者机构：Ilmenau Univ Technol Weimarer Str 25 D-98693 Ilmenau Germany 

出 版 物：《MATHEMATICAL PROGRAMMING》 (数学规划)

年 卷 期：2017年第164卷第1-2期

页      面：29-53页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 

主　　题：Multiobjective programming Stability Confidence sets Estimated functions Relaxation Markowitz model 

摘      要：Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears-the approximate problem . Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.