A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere

In this paper, we propose a hybrid second-order method for homogenouspolynomial optimization over the unit sphere in which the new iterate is generated byemploying the second-order information of the objective function. To guarantee theconvergence, we recall the shifted power method when the second-order method doesnot make an improvement to the objective function. As the Hessian of the objectivefunction can easily be computed and no line search is involved in the second-orderiterative step, the method is not time-consuming. Further, the new iterate is generatedin a relatively larger region and thus the global maximum can be likely obtained. Thegiven numerical experiments show the efficiency of the proposed method.