摘要：The trust region(TR) method for optimization is a class of effective methods.The conic model can be...The trust region(TR) method for optimization is a class of effective methods.The conic model can be regarded as a generalized quadratic model and it possesses the good convergence properties of the quadratic model near the minimizer.The Barzilai and Borwein(BB) gradient method is also an effective method,it can be used for solving large scale optimization problems to avoid the expensive computation and storage of matrices.In addition,the BB stepsize is easy to determine without large computational efforts.In this paper,based on the conic trust region framework,we employ the generalized BB stepsize,and propose a new nonmonotone adaptive trust region method based on simple conic model for large scale unconstrained optimization.Unlike traditional conic model,the Hessian approximation is an scalar matrix based on the generalized BB stepsize,which resulting a simple conic model.By adding the nonmonotone technique and adaptive technique to the simple conic model,the new method needs less storage location and converges faster.The global convergence of the algorithm is established under certain conditions.Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems.显示全部
摘要：基于非单调的frame概念，提出了一个求解无约束最优化问题的直接搜索共轭梯度算法．该算法不使用充分下降条...基于非单调的frame概念，提出了一个求解无约束最优化问题的直接搜索共轭梯度算法．该算法不使用充分下降条件而能够在网格（grid）之外进行搜索，这一点不同于Gss（generating set search）算法框架，后者为了实现网格之外的搜索必须使用充分下降条件或者移动网格（moving grids）技术或者有理点阵（rational lattice）技术．在一定的条件下，该算法的全局收敛性也得到了证明．数值试验表明，该算法是有效的．显示全部
