Equivalent Lagrangians for generalized fractional programming
type: Item
instance of: scholarly article
title: Equivalent Lagrangians for generalized fractional programming
zbMATH Open document ID: 0806.90118
author: Viveka Kumar
author: Suresh Chandra
published in: Opsearch
publication date: 1995-02-19T00:00:00Z
review text: Consider the generalized fractional programming problem \[ \min_{x\in S} \max_{1\leq i\leq p} (f_ i(x)/h_ i(x)), \] where \(S= \{x: x\in X,\;g_ j(x)\leq 0,\;j=1,2,\dots,m\}\). A Lagrangian \[ L(x,w,u)= {w^ T f(x)+ u^ T g(x)\over w^ T h(x)}, \] is introduced and appropriate saddlepoint and duality results established. The relationship of \(L(x,w,u)\) to another Lagrangian \[ GX(x,u)= \max_{1\leq i\leq p} (f_ i(x)/h_ i(x))+ \sum^ m_{i=1} u_ j \max_{1\leq i\leq p} (g_ i(x)/h_ i(x)), \] recently introduced in the literature is discussed. The advantages of \(L(x,w,u)\) over \(GX(x,u)\) is pointed out.
Mathematics Subject Classification ID: 90C32
zbMATH DE Number: 444903
zbMATH Keywords: minmax
zbMATH Keywords: generalized fractional programming
zbMATH Keywords: saddlepoint
zbMATH Keywords: duality
reviewed by: Bertram Mond
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 444903