ABSTRACT

To solve a large-scale unconstrained optimization problem, in this paper we propose a class of spectral three-term conjugate gradient methods. We indicate that the proposed class, in fact, generates sufficient descent directions and also fulfill Dai–Liao conjugacy condition. We prove the global convergence of the presented class for either uniformly convex or general smooth functions under some suitable conditions, in detail. Finally, in a set of numerical experiments which contains eight conjugate gradient methods and 260 standard problems, we illustrate the efficiency and effectiveness of our class.

中文翻译：

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用于大规模优化的新的充分下降谱三项共轭梯度类的全局收敛

摘要

为了解决大规模无约束优化问题，本文提出了一类谱三项共轭梯度方法。我们表明，所提出的类实际上产生了足够的下降方向，并且还满足 Dai-Liao 共轭条件。我们详细地证明了在一些合适的条件下，所提出的类对于均匀凸函数或一般光滑函数的全局收敛性。最后，在一组包含八种共轭梯度方法和 260 个标准问题的数值实验中，我们说明了我们课程的效率和有效性。