Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices: Approximation and applications

Yong Xia; Longfei Wang; Shu Wang

doi:10.1016/j.orl.2017.11.010

Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices: Approximation and applications

Yong Xia^*
, Longfei Wang
, Shu Wang

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University
North China Institute of Science & Technology

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The problem of maximizing the sum of two generalized Rayleigh quotients and the total least squares problem with nonsingular Tikhonov regularization are reformulated as a class of sum-of-linear-ratios minimizing over the cone of symmetric positive semidefinite matrices, which is shown to have a Fully Polynomial Time Approximation Scheme.

Original language	English
Pages (from-to)	76-80
Number of pages	5
Journal	Operations Research Letters
Volume	46
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2017.11.010
State	Published - Jan 2018

Keywords

FPTAS
Fractional programming
Rayleigh quotient
Semidefinite programming
Total least squares

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10.1016/j.orl.2017.11.010

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title = "Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices: Approximation and applications",

abstract = "The problem of maximizing the sum of two generalized Rayleigh quotients and the total least squares problem with nonsingular Tikhonov regularization are reformulated as a class of sum-of-linear-ratios minimizing over the cone of symmetric positive semidefinite matrices, which is shown to have a Fully Polynomial Time Approximation Scheme.",

keywords = "FPTAS, Fractional programming, Rayleigh quotient, Semidefinite programming, Total least squares",

author = "Yong Xia and Longfei Wang and Shu Wang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = jan,

doi = "10.1016/j.orl.2017.11.010",

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AU - Xia, Yong

AU - Wang, Longfei

AU - Wang, Shu

PY - 2018/1

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N2 - The problem of maximizing the sum of two generalized Rayleigh quotients and the total least squares problem with nonsingular Tikhonov regularization are reformulated as a class of sum-of-linear-ratios minimizing over the cone of symmetric positive semidefinite matrices, which is shown to have a Fully Polynomial Time Approximation Scheme.

AB - The problem of maximizing the sum of two generalized Rayleigh quotients and the total least squares problem with nonsingular Tikhonov regularization are reformulated as a class of sum-of-linear-ratios minimizing over the cone of symmetric positive semidefinite matrices, which is shown to have a Fully Polynomial Time Approximation Scheme.

KW - FPTAS

KW - Fractional programming

KW - Rayleigh quotient

KW - Semidefinite programming

KW - Total least squares

UR - https://www.scopus.com/pages/publications/85036642713

U2 - 10.1016/j.orl.2017.11.010

DO - 10.1016/j.orl.2017.11.010

M3 - 文章

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SN - 0167-6377

VL - 46

SP - 76

EP - 80

JO - Operations Research Letters

JF - Operations Research Letters

IS - 1

ER -

Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices: Approximation and applications

Abstract

Keywords

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