文档介绍：: 第一章t给出了一类新的非单调统一线搜索技术,在一定条件下,. 第二章:通常的线搜索算法中,,其中的参数可以根据当前点的信息进行调节。将该技术应用到记忆梯度法,数值结果表明了算法的有效性. 第三章;谱梯度法是求解大规模问题的一类有效算法,但由于谱梯度方向可能不是下降方向,,并分析了其收敛性和数值效果. 第四章:本章将第一章提出的非单调线搜索技术推广到边界约束优化问题,并将之与谱投影梯度法进行结合提出了一种边界约束优化问题的新算法,. 第五章:,我们利用光滑技术,将扩展线性互补同题转化为一个光滑方程组,分析了该等价转化的一些性质。透一步的,我们给出了求解该光滑方程组的非单调Newton算法并分析了其全局与局部收敛性. 第六章:本部分考虑等式约束优化问题的一类非单调信赖域方法。在一定条件下, 不仅获得了算法的全局收敛性,而且获得了局部超线性收敛性. 关键词:非单谓算法,收敛,无约束优化,约束优化,共轭梯度,谱梯度,扩展互补问题,价值函数,信赖域同济大学博士后研究工作报告 Abstract This thesis we consider some classesofnonmonotone numerical methods and their applications inoptimization plementarity thesisincludes sixparts: Chapter 1:Inthischapter,we give anew calssofnonmonotone linesearch technique. under certain conditions,we prove thatsome wellknown nonmonotone linesearch sun8 as nonmonotone Arimijo linesearch,Goldstein line search andWolfe linesearch are special case ofthe apply thismethod tosolving theunconstrained optimization and obtain theglobal convergnce under weak tests with Newton and memoryless quasi-Newton methods show theefficiency oftheproposed method. Chapter 2:In the traditional parameter associated with thestepsize isgiven randomly while independe(1 on the current iteration this chaper,we propose an adaptive nonmonotone linesearch technique where theparameter call beadjusted according themethod with memory gradient method tosolvetheunconstrained optimization and numerical tests are given. Chapter 3:Spectralgradient method andconjugategradient method are very eifec- tivemethods forlarge scaleproblem,but sincethespectralgradient direction may not be 8descrease direction,one should employ th