一类复合不可微规划的信赖域算法

提出了求解带线性的束的复不可微规划的信赖域算法,并证明了它的收敛性。     

求解一般约束优化问题的修正BFGS信赖域算法

借鉴无约束优化问题的BFGS信赖域算法,建立了非线性一般约束优化问题的BFGS信赖域算法,并证明了算法的全局收敛性．数值实验表明,算法是有效的．     

一类优化问题的非单调信赖域算法

本文提出了一类带不等式约束和简单边界的非线性优化问题的非单调信赖域算法,在一定的条件下,证明了算法的全局收敛性,并通过数值实验验证了算法的合理性。     

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．     

一类新的信赖域算法的全局收敛性

本文对于无约束最优化问题提出了一类非单调的信赖域算法，它是通常的单调信赖域算法的推广。当目标函数是有下界的连续可微函数，而且它的二阶导数的近似的模是线性地依赖于迭代次数时，我们证明了新算法的整体收敛性。     

信赖域方法的收敛性

信赖域方法的收敛性袁亚湘（中国科学院计算中心）ＯＮＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＴＲＵＳＴＲＥＧＩＯＮＡＬＧＯＲＩＴＨＭＳ￥ＹｕａｎＹａ－ｘｉａｎｇ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒＡｃａｄｅｍｉａＳｉｎｉｃａ）Ａｂｓｔｒａｃｔ：Ｔｒｕｓｔｒｅｇｉｏ...     

信赖域策略的内点投影既约Hessian方法解非线性约束优化

A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed. In order to deal with large problems,a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem. The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint. Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems. By adopting the l1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill-conditioned cases.     

一类新的非单调信赖域算法及其收敛性

利用非单调性,邓乃扬等提出了一类具有强收敛性质的非单调信赖型算法,为了保证算法的收敛性,他们假定以下两个条件成立;（１）信赖域半径（△ｋ）有上界;（２）对所有ｋ有∥ｓｋ∥≤ｃ∥ｇｋ∥,其中ｓｋ＝ｘｋ＋１－ｘｋ,ｇｋ为ｆ（ｔ）在ｘｋ处的梯度,ｃ〉０随后,柯小伍,韩继业从另一角度了提出了一类非调信赖域型算法,尽管他们未利用条件,但仍假定条件（２）成立,在本文中,我们提出了一类新的非单调信赖域算法,在没     

无约束多目标规划的非单调信赖域算法

本提出了无约束多目标规划的一类非单调信赖域算法，并证明了算法的全局收敛性。     

A Nonmonotone Trust Region Algorithm for Nonlinear Optimization Subject to General Constraints

In this paperwe present a nonmonotone trust region algorthm for general nonlinear constrained optimization problems.The main idea of this paper is to combine Yuan‘‘‘‘s technique[1]with a nonmonotone method similar to Ke and Han[2].This new algorithm may not only keep the robust properties of the algorithm given by Yuan,but also have some advantages led by the nonmonotone technique.Under very mild conditions,global convergence for the algorithm is given.Numerical experiments demostrate the efficency of the algorithm.     

带非线性不等式约束优化问题的信赖域算法

借助于KKT条件和NCP函数,提出了求解带非线性不等式约束优化问题的信赖域算法.该算法在每一步迭代时,不必求解带信赖域界的二次规划子问题,仅需求一线性方程组系统.在适当的假设条件下,它还是整体收敛的和局部超线性收敛的.数值实验结果表明该方法是有效的.     

一种约束非光滑优化问题的信赖域算法

提出了一种易实施的求解带线性约束的非光滑优化问题的信赖域算法，并在一定的条件下证明了该算法所产生的迭代序列的任何聚点都是原问题的稳定点．有限的数值例子表明，该方法是行之有效的．     

一类约束非光滑优化的非单调信赖域算法

提出了求解一类带一般凸约束的复合非光滑优化的信赖域算法 .和通常的信赖域方法不同的是 :该方法在每一步迭代时不是迫使目标函数严格单调递减 ,而是采用非单调策略 .由于光滑函数、逐段光滑函数、凸函数以及它们的复合都是局部Lipschitz函数 ,故本文所提方法是已有的处理同类型问题 ,包括带界约束的非线性最优化问题的方法的一般化 ,从而使得信赖域方法的适用范围扩大了 .同时 ,在一定条件下 ,该算法还是整体收敛的 .数值实验结果表明 :从计算的角度来看 ,非单调策略对高度非线性优化问题的求解非常有效     

等式约束优化非单调信赖域算法

设计了一个新的求解等式约束优化问题的非单调信赖域算法.该算法不需要罚函数也无需滤子.在每次迭代过程中只需求解满足下降条件的拟法向步及切向步.新算法产生的迭代步比滤子方法更易接受,计算量比单调算法小.在一般条件下,算法具有全局收敛性.     

无约束不可微观划的信赖域算法

提出了一种易实施的求无约束不可微规划的信赖域算法,并在一定条件下证明了该算法所产生的点列的任何聚点都是原问题的稳定点。     

基于信赖域技术的处理带线性约束优化的内点算法

基于信赖域技术,本文提出了一个求解带线性等式和非负约束优化问题的内点算法,其特点是:为了求得搜索方向,算法在每一步迭代时仅需要求解一线性方程组系统,从而避免了求解带信赖域界的子问题,然后利用非精确的Armijo线搜索法来得到下一个迭代内点. 从数值计算的观点来看,这种技巧可减少计算量.在适当的条件下,文中还证明了该算法所产生的迭代序列的每一个聚点都是原问题的KKT点.     

Quadratic Convergence of a Primal-Dual Interior Point Method for Degenerate Nonlinear Optimization Problems

Recently studies of numerical methods for degenerate nonlinear optimization problems have been attracted much attention. Several authors have discussed convergence properties without the linear independence constraint qualification and/or the strict complementarity condition. In this paper, we are concerned with quadratic convergence property of a primal-dual interior point method, in which Newton’s method is applied to the barrier KKT conditions. We assume that the second order sufficient condition and the linear independence of gradients of equality constraints hold at the solution, and that there exists a solution that satisfies the strict complementarity condition, and that multiplier iterates generated by our method for inequality constraints are uniformly bounded, which relaxes the linear independence constraint qualification. Uniform boundedness of multiplier iterates is satisfied if the Mangasarian-Fromovitz constraint qualification is assumed, for example. By using the stability theorem by Hager and Gowda (1999), and Wright (2001), the distance from the current point to the solution set is related to the residual of the KKT conditions.By controlling a barrier parameter and adopting a suitable line search procedure, we prove the quadratic convergence of the proposed algorithm.     

An ODE-Based Trust Region Filter Algorithm for Unconstrained Optimization

In this article, an ODE-based trust region filter algorithm for unconstrained optimization is proposed. It can be regarded as a combination of trust region and filter techniques with ODE-based methods. Unlike the existing trust-region-filter methods and ODE-based methods, a distinct feature of this method is that at each iteration, a reduced linear system is solved to obtain a trial step, thus avoiding solving a trust region subproblem. Under some standard assumptions, it is proven that the algorithm is globally convergent. Preliminary numerical results show that the new algorithm is efficient for large scale problems.