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非线性不等式约束最优化快速收敛的可行信赖域算法 总被引:5,自引:0,他引:5
In this paper,by combining the trust region technique with the generalized gradient projection.a new trust region algorithm with feasible iteration points is presented for nonlinear inequality constrained optimization,and its trust region is a general compact set containing the origion as an inteior point.No penalty function is used in the algorithm,and it is feasible descent .Under suitable assumptions,the algorithm is proved to possess global and strong convergence as well as superlinear and quadratic convergence.Some numerical results are reported. 相似文献
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具不等式约束变分不等式的信赖域算法 总被引:1,自引:0,他引:1
1 引 言令X是Rn 中的非空闭凸集 ,F :X→Rn 是连续映射 ,〈· ,·〉表示Rn 中的内积 有限维变分不等式问题 (以下简称变分不等式问题 ,记为VIP或VI(X ,F) ) :就是求x ∈Rn,使x ∈X且 x ∈X ,〈F(x ) ,x -x 〉≥ 0 . ( 1 )在X =Rn+ 的特殊情形下 ,( 1 )变为非线性互补问题 (记为NCP或NCP(F) ) :就是求x ∈Rn,使x ≥ 0 ,F(x ) ≥ 0 ,且〈x ,F(x )〉 =0 . ( 2 ) 变分不等式长期以来一直用于阐述和研究经济学、控制论、交通运输等领域中出现的各种平衡模型 近二十年来 ,变分不等式及其… 相似文献
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带非线性不等式约束优化问题的信赖域算法 总被引:1,自引:0,他引:1
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. 相似文献
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一类新的信赖域算法的全局收敛性 总被引:22,自引:1,他引:22
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。 相似文献
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本文对线性不等式约束的非线性规划问题提出了一类信赖域算法,证明了算法所产生的序列的任一聚点为Kuhn-Tucker点,并讨论了子问题求解的有效集方法. 相似文献
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本文通过对无约束优化ODE算法的信赖域分析,提出了约束优化问题的曲线搜索信赖域算法,给出了算法步骤,并讨论了该算法的全局收敛性。 相似文献
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结合利用Hessian阵的特征值性质,本文提出求解信赖域子问题的一种双割线折线法,它不同于Powell的单折线,Dennis的双折线和赵英良的切线单折线.在适当条件下,分析双割线折线路径的性质,且证明了算法的收敛性.数值试验表明,这种新算法是有效且可行的. 相似文献
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一类Dogleg路径信赖域方法 总被引:1,自引:0,他引:1
本文提出一类折线搜索的信赖域方法,用于解无约束最优化问题,这些方法通过对一般对称矩阵的Bunch-Parlett分解来产生搜索路径,我们证明在一些较弱的条件下,算法是整体收敛的,对一致凸函数,是二次收敛的,并且在由算法得到的点列的任意聚点上,连续可微的目标函数的Hesse阵都是正定或半正定的,一些数值结果表明这种新的方法是非常有效的。 相似文献
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On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization 下载免费PDF全文
A trust-region sequential quadratic programming (SQP) method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the transposition of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported. 相似文献
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Jinyan Fan 《Computational Optimization and Applications》2006,34(2):215-227
In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The
new method preserves the global convergence of the traditional trust region methods in which the trust region radius will
be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition
which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic.
Finally, some numerical results are given.
This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong
University, and E-Institute of Computational Sciences of Shanghai Universities.
An erratum to this article is available at . 相似文献
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该文给出了一个求解非线性系统的信赖域方法.主要思想是通过引入松弛变量,将问题等价地转化为带非负约束的最优化问题.作者利用有效集策略,在每次迭代中只需求解一个低维的信赖域子问题,该信赖域子问题是通过截断共轭梯度法来近似求解的.在较弱的条件下,获得了一个更一般的收敛性结果. 相似文献
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In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient. 相似文献
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设f:R^n→R为实值拟可微函数,x∈domf,则f在x点沿方向d∈R^n的方向导数表示为 相似文献