A Three-Term Gradient Descent Method with Subspace Techniques

We proposed a three-term gradient descent method that can be well applied to address the optimization problems in this article. The search direction of the obtained method is generated in a specific subspace. Specifically, a quadratic approximation model is applied in the process of generating the search direction. In order to reduce the amount of calculation and make the best use of the existing information, the subspace was made up of the gradient of the current and prior iteration point and the previous search direction. By using the subspace-based optimization technology, the global convergence result is established under Wolfe line search. The results of numerical experiments show that the new method is effective and robust.