An Adaptive Projection Gradient Method for Solving Nonlinear Fractional Programming

In this study, we focus on solving the nonlinear fractional optimization problem in which the numerator is smooth convex and the denominator is smooth concave. To achieve this goal, we develop an algorithm called the adaptive projection gradient method. The main advantage of this method is that it allows the computations for the gradients of the considered functions and the metric projection to take place separately. Moreover, an interesting property that distinguishes the proposed method from some of the existing methods is the nonincreasing property of its step-size sequence. In this study, we also prove that the sequence of iterates that is generated by the method converges to a solution for the considered problem and we derive the rate of convergence. To illustrate the performance and efficiency of our algorithm, some numerical experiments are performed.