The spectral conjugate gradient methods are very interesting and have been proved to be effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate gradient method is proposed to solve large-scale unconstrained optimisation problems. Motivated by the advantages of approximate optimal stepsize strategy used in the gradient method, we design a new scheme for the choices of the spectral and conjugate parameters. Furthermore, the new search direction satisfies the spectral property and sufficient descent condition. Under some suitable assumptions, the global convergence of the developed method is established. Numerical comparisons show better behaviour of the proposed method with respect to some existing methods for a set of 130 test problems.

中文翻译：

---

大规模无约束优化的新谱共轭梯度法

频谱共轭梯度方法非常有趣，并已证明对于严格凸二次最小化有效。本文提出了一种新的谱共轭梯度法来解决大规模无约束优化问题。受梯度方法中使用的近似最佳步长调整策略优点的启发，我们设计了一种用于选择光谱和共轭参数的新方案。此外，新的搜索方向满足光谱特性和足够的下降条件。在适当的假设下，建立了所开发方法的全局收敛性。数值比较表明，相对于针对130个测试问题的一些现有方法，该方法具有更好的性能。