Minimization of the ratio of functions defined as sums of the absolute values

H. Konno; K. Tsuchiya; R. Yamamoto

doi:10.1007/s10957-007-9284-z

Minimization of the ratio of functions defined as sums of the absolute values

H. Konno, K. Tsuchiya, R. Yamamoto

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

8 Citations (Scopus)

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	https://doi.org/10.1007/s10957-007-9284-z
Publication status	Published - 2007 Dec
Externally published	Yes

Keywords

0-1 integer programming
Branch and bound algorithms
Fractional programming problems
Global optimization
Portfolio optimization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Access to Document

10.1007/s10957-007-9284-z

Fingerprint Dive into the research topics of 'Minimization of the ratio of functions defined as sums of the absolute values'. Together they form a unique fingerprint.

Cite this

@article{d47ce2de418a4f2aa4014b43eaa28ea2,

title = "Minimization of the ratio of functions defined as sums of the absolute values",

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.",

keywords = "0-1 integer programming, Branch and bound algorithms, Fractional programming problems, Global optimization, Portfolio optimization",

author = "H. Konno and K. Tsuchiya and R. Yamamoto",

note = "Funding Information: The research of the first author was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Culture and Sports of the Government of Japan, B(2) 15310122 and 15656025.",

year = "2007",

month = dec,

doi = "10.1007/s10957-007-9284-z",

language = "English",

volume = "135",

pages = "399--410",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Minimization of the ratio of functions defined as sums of the absolute values

AU - Konno, H.

AU - Tsuchiya, K.

AU - Yamamoto, R.

N1 - Funding Information: The research of the first author was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Culture and Sports of the Government of Japan, B(2) 15310122 and 15656025.

PY - 2007/12

Y1 - 2007/12

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 -