Solving A Fractional Program with Second Order Cone Constraint

Our main interest in the present article is to consider a fractional program with both linear and quadratic equation in numerator and denominator with second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a second order cone programming (SOCP) problem. For the quadratic fractional case, using a relaxation, then the problem is reduced to a semi-definite optimization (SDO) ) program. The problem is solved with SDO relaxation and the obtained results are compared with the interior point method (IPM), sequential quadratic programming approach (SQP), active set, genetic algorithm. It is observe that the SDO relaxation method is much more accurate and faster than the other methods. Finally, two numerical examples are given to demonstrate the procedure for the proposed method to guarantee the approach.