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

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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 -