In this paper, a new conjugacy condition is established to solve unconstrained optimization problems based on a new quasi-Newton equation. We present a modified Dai–Liao conjugate gradient method to solve unconstrained optimization problems with a new value of the parameter t based on the new conjugacy condition. The presented algorithm has the following properties: (i) the modified Dai–Liao conjugate gradient method considers both the gradient and function value information. (ii) The global convergence is achieved for the modified Dai–Liao conjugate gradient method under some suitable assumptions. (iii) Numerical experiments on unconstrained optimization problems and image restoration problems are conducted, and the numerical results show that our method is efficient.

本文基于一个新的拟牛顿方程，建立了一个新的共轭条件来求解无约束优化问题。我们提出了一种改进的Dai-Liao共轭梯度方法，以基于新的共轭条件用参数t的新值来解决无约束优化问题。所提出的算法具有以下特性：（i）改进的Dai-Liao共轭梯度法同时考虑了梯度和函数值信息。（ii）在某些适当的假设下，采用改进的戴辽共轭梯度法实现了全局收敛。（iii）进行了无约束优化问题和图像恢复问题的数值实验，数值结果表明我们的方法是有效的。