A New Three-Term Conjugate Gradient Method for Unconstrained Optimization with Applications in Portfolio Selection and Robotic Motion Control

Three-term conjugate gradient method is one of the efficient method for solving unconstrained optimization models. In this paper, we propose a new three-term conjugate gradient method with a new search direction structure. A remarkable feature of the proposed method is that independent of the line search procedure, the search direction always satisfies the sufficient descent condition. The global convergence properties of the proposed method is established under the strong Wolfe line search by assuming that the objective function is Lipschitz continuous. Numerical results indicate that our proposed method is efficient and robust, thus effective in solving unconstrained optimization models. In addition, the proposed method also considered practical application problem in portfolio selection and robotic motion control.