Separable convex programs with ratio constraints over a directed tree
type: Item
instance of: scholarly article
title: Separable convex programs with ratio constraints over a directed tree
zbMATH Open document ID: 0771.90080
DOI: 10.1016/0167-6377(92)90078-H
author: Christopher S. Tang
author: Carlton H. Scott
published in: Operations Research Letters
publication date: 1993-01-16T00:00:00Z
review text: The authors develop a simple procedure for solving separable convex programs with ratio constraints in the form \[ \text{Min }\sum_{j\in N} f_ j(x_ j)\text{ s.t. } x_ i\geq r_{i_ j} x_ j,\;(i,j)\in A,\;\ell_ i\leq x_ i\leq u_ i,\;i\in N,\leqno(\text P) \] where the \(x_ i\)'s are the decision variables, \(\ell_ i\) and \(u_ i\) are the lower and upper bounds on each decision variable, \(N\) is the set of nodes and \(A\), called the arcs, is a subset of \(N\times N\). The functions \(f_ j(.)\) are assumed to be strictly convex and differentiable. The authors notice that this procedure is an extension of the technique developed by the second author [Manage. Sci. 36, No. 11, 1407-1412 (1990; Zbl 0727.90060)]. It is claimed that such problems arise in production planning, regression analysis and other related areas.
reviewed by: R. N. Kaul
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 90C90
zbMATH DE Number: 92009
zbMATH Keywords: directed tree
zbMATH Keywords: separable convex programs
zbMATH Keywords: ratio constraints
zbMATH Keywords: production planning
zbMATH Keywords: regression analysis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 92009