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 -