A fractional programming algorithm based on conic quasi-Newton trust region method for unconstrained minimization

In this paper, we present a new algorithm for quasi-Newton type trust region subproblem with a conic model solving unconstrained optimization problems. In the algorithm, we propose to use the method of dealing with fractional programming into the conic model as the conic model is of fractional form and the method can find the real solution of subproblem not an approximate solution like the available method. This new approach can be easily generalized to any optimization method which its approximate subproblem with fractional expression, whose approximate effectiveness to the class of highly vibrating objective functions is superior to that of the normal quadratic model. This idea is what the author want to develop through the conic model as a special example in the paper. The preliminary numerical test shows that the new method is more effective.