{"title":"Monotone limits in linear programming problems","authors":"M. Yamasaki","doi":"10.32917/HMJ/1206138223","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to investigate the behavior of values of linear programming problems under some monotone variations of objective functions and constraints. More precisely, let X and Y be real linear spaces paired under the bilinear functional ((,))i, and let Z and W be real linear spaces paired under the bilinear functional ( ( , ) ) 2 A (linear) program for these paired spaces is a quintuple (A, P, Q, j 0 ? z0). In this quintuple, A is a linear transformation from X into Z, P is a convex cone in X, Q is a convex cone in Z, γ0 is an element of Y and z0 is an element of Z. The set S of feasible solutions for the program and the value M of the program are defined by","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"2014 1","pages":"249-258"},"PeriodicalIF":0.0000,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/HMJ/1206138223","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The aim of this paper is to investigate the behavior of values of linear programming problems under some monotone variations of objective functions and constraints. More precisely, let X and Y be real linear spaces paired under the bilinear functional ((,))i, and let Z and W be real linear spaces paired under the bilinear functional ( ( , ) ) 2 A (linear) program for these paired spaces is a quintuple (A, P, Q, j 0 ? z0). In this quintuple, A is a linear transformation from X into Z, P is a convex cone in X, Q is a convex cone in Z, γ0 is an element of Y and z0 is an element of Z. The set S of feasible solutions for the program and the value M of the program are defined by