This article presents a new hybrid conjugate gradient (CG) algorithm for solving unconstrained optimization problem. The search direction is defined as a combination of Hestenes–Stiefel (HS) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) quasi-Newton direction. In addition, the search direction is descent and bounded. The global convergence of the algorithm is obtained under the Wolfe-type and Armijo-type line searches. Numerical experiments on some benchmark test problems is carried out to depict the efficiency and robustness of the hybrid algorithm. Furthermore, a practical application of the algorithm in motion control of robot manipulator and image restoration is provided.
- Global convergence
- Line search
- Three-term conjugate gradient method
- Unconstrained optimization