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

H. Konno, K. Tsuchiya, Rei Yamamoto

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)399-410
Number of pages12
JournalJournal of Optimization Theory and Applications
Volume135
Issue number3
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

Fingerprint

Absolute value
Fractional Programming
Affine Function
Branch and Bound Algorithm
Integer programming
Large-scale Problems
Integer Programming
Fractional
Objective function
Linearly
Optimization
Demonstrate
Fractional programming
Branch and bound algorithm

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 journalArticle

Konno, H. ; Tsuchiya, K. ; Yamamoto, Rei. / Minimization of the ratio of functions defined as sums of the absolute values. In: Journal of Optimization Theory and Applications. 2007 ; Vol. 135, No. 3. pp. 399-410.
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