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 functio...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.展开更多
基金the National Natural Science Foundation of China(No.11671228).
文摘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.
