Based on the work of Powell, Dennis and Zhao Yingliang, the first part of this thesis puts forward the hybrid method to solve the subproblem. It is applied to deal with the ordinary unconstrained optimization problem.

• 基于Powell的单折线法、Dennis的双折线法和赵英良的切线单折线法，本文第一部分提出了解信赖域子问题的混合折线法，并用于解一般的无约束优化问题。