A New Method for Solving Unconstrained Optimization Problems.

In this paper, a new conjugate gradient formula β^New_k is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with some line searches such as the exact line search, the Grippo-Lucidi line search and the Wolfe-Powell line search are discussed. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula β^New_k ⩾ 0, and the search directions d_k which are generated by the given β^New_k under the strong Wolfe-Powell line search satisfy the sufficient descent condition. Preliminary numerical results show that the proposed methods are efficient. [ABSTRACT FROM AUTHOR]