大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法的全局收敛性

本文在ZhangH．C．的非单调线搜索规则基础上，结合ShiZ．J．大步长线搜索技巧提出了新的大步长的非单调线搜索规则，设计了求解无约束最优化问题的大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法，在△f（x）一致连续的条件下给出了算法的全局收敛性和超线性收敛性分析．数值例子表明算法是有效的，适合求解大规模问题．     

新非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法

本文设计了求解无约束最优化问题的新的非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法.新的步长规则类似于Grippo非单调线搜索规则并包含Grippo非单调线搜索规则作为特例.新的步长规则在每一次线搜索时得到一个相对于Grippo非单调线搜索规则的较大步长,同时保证算法的全局收敛性.数值例子表明算法是有效的,适合求解大规模问题.     

基于非单调线搜索非拟牛顿法的全局收敛性

本文就非拟牛顿法在无约束最优化问题上，对采用非单调线搜索的情况下是否具有全局收敛性进行了研究，在目标函数满足一致凸的条件下，证明了非拟牛顿族是全局收敛的．     

一类非单调保守BFGS算法研究

基于非单调线搜索在寻求优化问题最优解中的优越性,提出了一类新的非单调保守BFGS算法.同已有方法不同,该算法中用来控制非单调性程度的算法参数不是取固定值,而是利用已有目标函数和梯度函数的信息自动调整其取值,以改善算法的数值表现.在合适的假设条件下,建立了新的非单调保守BFGS算法的全局收敛性.用基准测试优化问题测试了算...     

BFGS算法对非凸函数优化问题的收敛性

ＢＦＧＳ算法是无约束最优化中最著名的数值算法之一,对非凸函数ＢＦＧＳ算法是否具有整体收敛性,这是一个ｏｐｅｎ问题,本文考虑Ｗｏｌｆｏ线搜索下目标函数非凸的ＢＦＧＳ算法,我们给出一个使该算法收敛的充分条件。     

一类非单调修正PRP算法的全局收敛性

本文给出一类非单调线性搜索下的修正PRP算法,该方法保证每次迭代中的搜索方向是充分下降的.在较弱的条件下,我们证明了此类非单调修正PRP算法具有全局收敛性.     

一类带非单调线搜索的信赖域算法

通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某...     

一种修改的非单调线搜索SQP算法

提出了一种解非线性规划问题的修改的非单调线搜索算法,并给出了它的全局收敛性证明.不需要用罚函数作为价值函数,也不用滤子和可行性恢复阶段.该算法是基于多目标优化的思想一个迭代点被接受当且仅当目标函数值或是约束违反度函数值有充分的下降.数值结果与LANCELOT作了比较,表明该算法是可靠的.     

约束最优化的一个使用非单调线搜索的超线性收敛算法

Abstract. In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.     

一类带线搜索的非单调信赖域算法

本文对于无约束最优化问题提出了一类新的非单调信赖域算法．与通常的非单调信赖域算法不同，当试探步不成功时，并不重解信赖域子问题，而采用非单调线搜索，从而减小了计算量．在适当的条件下，证明了此算法的全局收敛性．     

The Global Convergence of Self-Scaling BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.     

Global Convergence Analysis of a New Nonmonotone BFGS Algorithm on Convex Objective Functions

In this paper, a new nonmonotone BFGS algorithmfor unconstrained optimization is introduced. Under mild conditions,the global convergence of this new algorithm on convex functions isproved. Some numerical experiments show that this new nonmonotoneBFGS algorithm is competitive to the BFGS algorithm.     

Global Convergence of the Broyden‘’s Class of Quasi—Newton Methods with Nonmonotone Linesearch

In this paper,the Broyden class of quasi-Newton methods for unconstrained optimization is inves-tigated.Non-monotone linesearch procedure is introduced,which is combined with the Broyden‘s class.Under the convexity assumption on objective function,the global convergence of the Broyden‘s class is proved.     

结合广义Armijo步长搜索的超记忆梯度算法及其收敛特征

对无约束规划 ( P) :minx∈ Rnf ( x) ,其中 f ( x)是 Rn→ R1上的一阶连续可微函数 ,设计了一个超记忆梯度求解算法 ,并在去掉迭代点列 { xk}有界和广义 Armijo步长搜索下 ,讨论了算法的全局的收敛性 ,证明了算法具有较强的收敛性质     

结合Armijo步长搜索的一类新的记忆梯度算法及其收敛特征

对求解无约束规划的超记忆梯度算法中线搜索方向中的参数,给了一个假设条件,从而确定了它的一个新的取值范围,保证了搜索方向是目标函数的充分下降方向,由此提出了一类新的记忆梯度算法.在去掉迭代点列有界和Armijo步长搜索下,讨论了算法的全局收敛性,且给出了结合形如共轭梯度法FR,PR,HS的记忆梯度法的修正形式.数值实验表明,新算法比Armijo线搜索下的FR、PR、HS共轭梯度法和超记忆梯度法更稳定、更有效.     

解一类Hessian矩阵亏秩的修正BFGs算法及其局部Q-超线性收敛性

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下,给出了一类求解无约束优化问题的修正BFGS算法.算法的思想是对凸函数加上一个修正项,得到一个等价的模型,然后简化此模型得到一个修正的BFGS算法.文中证明了该算法是一个具有超线性收敛的算法,并且把修正的BFGS算法同Tensor方法进行了数值比较,证明了该算法对求解秩亏一的无约束优化问题更有效.     

结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.     

Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

In this paper, the continuously differentiable optimization problem min{f（x） ： x∈Ω}, where Ω ∈ R^n is a nonempty closed convex set, the gradient projection method by Calamai and More （Math. Programming, Vol.39. P.93-116, 1987） is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x^k} of bounded. Moreover, it is shown that, when f（x） is pseudo-convex （quasiconvex） function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method.     

一类新的共轭梯度法的全局收敛性

本文提出了一类与HS方法相关的新的共轭梯度法.在强Wolfe线搜索的条件下,该方法能够保证搜索方向的充分下降性,并且在不需要假设目标函数为凸的情况下,证明了该方法的全局收敛性.同时,给出了这类新共轭梯度法的一种特殊形式,通过调整参数ρ,验证了它对给定测试函数的有效性.     

局部误差的有界约束非线性方程组的非单调信赖域算法

本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率.