 Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear ProgrammingA. L. Soyster
Operations Research, 1973, vol. 21, issue 5, 1154-1157 Abstract: This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities, f i ( x ) ≦ b i , i = 1, 2, …, m , the feasible region is defined via set containment. Here n convex activity sets { K j , j = 1, 2, …, n } and a convex resource set K are specified and the feasible region is given by \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$X =\{x \in R^{n}\mid x_{1}K_{1} + x_{2}K_{2} + \cdots + x_{n}K_{n} \subseteq K, x_{j}\geq 0\}$$\end{document} where the binary operation + refers to addition of sets. The problem is then to find x̄ ∈ X that maximizes the linear function c · x . When the resource set has a special form, this problem is solved via an auxiliary linear-programming problem and application to inexact linear programming is possible. Date: 1973 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:21:y:1973:i:5:p:1154-1157 Access Statistics for this article More articles in Operations Research from INFORMS Contact information at EDIRC. |
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