Fractional programming with absolute-value functions

This paper considers a fractional functionals programming problem of the type: maximize z = Sigma(1)(n)C(j)\x(j)\ + alpha/Sigma(1)(n)d(j)\x(j)\ = beta subject to Ax = b. x is unrestricted. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of problems. However, this work presents the conditions under which simplex-type algorithms can be used to arrive at an optimal solution for a fractional programming problem with an absolute value objective function. (C) 2002 Elsevier Science B.V. All rights reserved.