Global solutions to fractional programming problem with ratio of nonconvex functions

N. Ruan; D. Y. Gao

doi:10.1016/j.amc.2014.08.060

Global solutions to fractional programming problem with ratio of nonconvex functions

N. Ruan, D. Y. Gao

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

6 Citations (Scopus)

Abstract

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rⁿ. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R² that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.

Original language	English
Pages (from-to)	66-72
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	255
DOIs	https://doi.org/10.1016/j.amc.2014.08.060
Publication status	Published - 15 Mar 2015
Externally published	Yes

Keywords

Canonical duality theory
Global optimization
Nonconvex fractional programming
Sum-of-ratios

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10.1016/j.amc.2014.08.060

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title = "Global solutions to fractional programming problem with ratio of nonconvex functions",

abstract = "This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rn. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.",

keywords = "Canonical duality theory, Global optimization, Nonconvex fractional programming, Sum-of-ratios",

author = "N. Ruan and Gao, \{D. Y.\}",

note = "Funding Information: This paper was partially supported by a grant (AFOSR FA9550–10-1–0487) from the US Air Force Office of Scientific Research. Dr. Ning Ruan was supported by a funding from the Australian Government under the Collaborative Research Networks (CRN) program. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc. All rights reserved. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "2015",

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doi = "10.1016/j.amc.2014.08.060",

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AU - Gao, D. Y.

N1 - Funding Information: This paper was partially supported by a grant (AFOSR FA9550–10-1–0487) from the US Air Force Office of Scientific Research. Dr. Ning Ruan was supported by a funding from the Australian Government under the Collaborative Research Networks (CRN) program. Publisher Copyright: © 2014 Elsevier Inc. All rights reserved. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015/3/15

Y1 - 2015/3/15

N2 - This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rn. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.

AB - This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rn. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.

KW - Canonical duality theory

KW - Global optimization

KW - Nonconvex fractional programming

KW - Sum-of-ratios

UR - https://www.scopus.com/pages/publications/84923816018

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DO - 10.1016/j.amc.2014.08.060

M3 - Article

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SN - 0096-3003

VL - 255

SP - 66

EP - 72

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Global solutions to fractional programming problem with ratio of nonconvex functions

Abstract

Keywords

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