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中文摘要：
为有效求解大规模无约束优化问题,本文基于RMFI共轭梯度法,结合Zhang H.C.非单调线搜索步长规则,提出了一类新的共轭梯度算法.在适当的条件下,证明了新算法的全局收敛性.数值算例表明,新算法比Zhang H.C.非单调规则下的标准RMFI方法收敛速度更快,更有效.同时,本文进一步研究了Zhang H.C.非单调线搜索步长规则的一个基于强迫函数的拓展模型,并从理论上证明了基于此拓展模型的新算法的全局收敛性.
英文摘要：
Based on the RMFI conjugate gradient method and the Zhang H. C. non-monotone line search method, a new kind of conjugate gradient methods for solving large scale uncon- strained optimization problems is presented. Under mild conditions, the proposed method with the Zhang H.C. line search method converges globally. Numerical results show that the new method is more efficient when compared with th RMFI method with the Zhang H. C. rule. In addition, we extend the Zhang H. C. non-monotone line search method by utilizing the forcing function, and theoretically, we have proved the new conjugate gradient methods＇ global conver- gence with the extended model.
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