TY - JOUR
T1 - Global solutions to fractional programming problem with ratio of nonconvex functions
AU - Ruan, N.
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 - http://www.scopus.com/inward/record.url?scp=84923816018&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.08.060
DO - 10.1016/j.amc.2014.08.060
M3 - Article
AN - SCOPUS:84923816018
SN - 0096-3003
VL - 255
SP - 66
EP - 72
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -