Abstract: In order to improve computational efficiency for unconstrained optimization problems, we proposed a new class of modified Hager-Zhang conjugate method, which possessed sufficient descent feature and trust region  trait without line search. The theoretical research results show that under some proper assumptions, the new algorithm not only converges globally for general function under weak Wolfe-Powell line search, but also has R-|linear convergence rate for uniformly convex functions. Numerical results show that the new algorithm performs better than the classical Hager-Zhang algorithm and its two classical modified algorithms.

Key words: unconstrained optimization, Hager-Zhang conjugate gradient method, sufficient descent feature, trust region trait, convergence