Abstract
This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.
| Original language | English |
|---|---|
| Pages (from-to) | 399-410 |
| Number of pages | 12 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 135 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2007 Dec 1 |
| Externally published | Yes |
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Keywords
- 0-1 integer programming
- Branch and bound algorithms
- Fractional programming problems
- Global optimization
- Portfolio optimization
ASJC Scopus subject areas
- Management Science and Operations Research
- Applied Mathematics
- Control and Optimization
Cite this
Minimization of the ratio of functions defined as sums of the absolute values. / Konno, H.; Tsuchiya, K.; Yamamoto, Rei.
In: Journal of Optimization Theory and Applications, Vol. 135, No. 3, 01.12.2007, p. 399-410.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minimization of the ratio of functions defined as sums of the absolute values
AU - Konno, H.
AU - Tsuchiya, K.
AU - Yamamoto, Rei
PY - 2007/12/1
Y1 - 2007/12/1
N2 - This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.
AB - This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.
KW - 0-1 integer programming
KW - Branch and bound algorithms
KW - Fractional programming problems
KW - Global optimization
KW - Portfolio optimization
UR - http://www.scopus.com/inward/record.url?scp=36148997292&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36148997292&partnerID=8YFLogxK
U2 - 10.1007/s10957-007-9284-z
DO - 10.1007/s10957-007-9284-z
M3 - Article
AN - SCOPUS:36148997292
VL - 135
SP - 399
EP - 410
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 3
ER -