| Unconstrained optimization is one of the most important branches of op-timization field, which is applied widely to engineering design, management control, finance service and so on. Effective numerical method is the key problem of unconstrained optimization research. Conjugate gradient method is a class of the effective method, which has been studied intensively and ap-plied to practice. This thesis discusses hybrid conjugate gradient methods for solving unconstrained smooth and non-smooth optimizations, respectively.First of all, for unconstrained smooth optimization, this thesis proposes a new hybrid conjugate gradient method based on conjugate gradient meth-ods of some famous scholars. The proposed method can generate a descent direction in each iteration without dependence of the fixed line search used. Under the standard Wolfe-Powell line search, the global convergence of the proposed method is proved. Some elementary numerical experiments are also reported to demonstrate the validity of the proposed method.Secondly, for unconstrained nonsmooth optimization which has been regarded of one of the difficulties of optimization field, according to the algorithmic thinking of [Li Q. OPTIMIZATION LETTERS,2013,7(3)], the aforementioned method for unconstrained smooth optimization can be improved properly to extend to unconstrained non-smooth convex optimiza-tion by combining inexact Moreau-Yosida regulation technique. This further proves that the generated search directions satisfy sufficient descent condition and bounded. And the global convergence is achieved under some assump-tion. |
