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1.
一个新的共轭投影梯度算法及其超线性收敛性 总被引:7,自引:0,他引:7
利用共轭投影梯度技巧,结合SQP算法的思想,建立了一个具有显示搜索方向的新算法,在适当的条件下,证明算法是全局收敛和强收敛的,且具有超线性收敛性,最后数值实验表明算法是有效的。 相似文献
2.
最优化两个拓广的SQP和SSLE算法模型及其超线性和二次收敛性 总被引:2,自引:0,他引:2
简金宝 《高校应用数学学报(A辑)》2001,16(4):435-444
给出一般约束最优化的序列二次规划(SQP)和序列线性方程组(SSLE)算法两个拓广的模型,详细分析和论证两个模型的局部超线性收敛性及二次收敛性条件,其中并不需要严格互补条件,拓广的模型及其收敛速度结果具有更广泛的适用性,为SQP和SSLE算法收敛速度的研究提供了更为完善和便利的理论基础。 相似文献
3.
一个等式约束问题的SQP方法及其收敛性 总被引:2,自引:0,他引:2
本文提出一个SQP算法,其效益函数为Flether^[1]提出的连续可微精确罚函数。该算法具有全局收敛性和超线性收敛速度,并且能自动调节罚参数,能有效地处理计算搜索方向的二次子规划的不可行问题。 相似文献
4.
时贞军 《高校应用数学学报(A辑)》1997,(2):209-218
本文考虑线性约束非线性规划问题,提出了一类共轭投影梯度法,证明了算法的全局收敛性,并对算法的二次终止性,超线性收敛特征进行了分析,算法的优点是(1)采用计算机上实现的Armijo线性搜索规则,(2)初始点不要求一定是可行点,可以不满足线性等式约束,(3)具有较快的收敛速度。 相似文献
5.
不等式约束优化一个新的SQP算法 总被引:5,自引:0,他引:5
本文提出了一个处理不等式约束优化问题的新的SQP算法.和传统的SQP算法相比,该算法每步只需求解一个仅含等式约束的子二次规划,从而减少了算法的计算工作量.在适当的条件下,证明算法是全局收敛的且具有超线性收敛速度.数值实验表明算法是有效的. 相似文献
6.
提出了一个处理等式约束优化问题新的SQP算法,该算法通过求解一个增广Lagrange函数的拟Newton方法推导出一个等式约束二次规划子问题,从而获得下降方向.罚因子具有自动调节性,并能避免趋于无穷.为克服Maratos效应采用增广Lagrange函数作为效益函数并结合二阶步校正方法.在适当的条件下,证明算法是全局收敛的,并且具有超线性收敛速度. 相似文献
7.
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非线性约束条件下的SQP可行方法 总被引:9,自引:0,他引:9
本文对非线性规划问题给出了一个具有一步超线性收敛速度的可行方法。由于此算法每步迭代均在可行域内进行,并且每步迭代只需计算一个二次子规划和一个逆矩阵,因而算法具有较好的实用价值。本文还在较弱的条件下证明了算法的全局收敛和一步超线性收敛性。 相似文献
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MBFGS修正在SQP算法中的应用—算法及其局部收敛性 总被引:1,自引:0,他引:1
本研究了SQP算法中保持矩阵正定性的方法.利用Li—Fukmshima提出的求解无约束问题的修正BFGS(MBFGS)公式,提出了求解等式约束问题的SQP算法.证明了若在问题的解处二阶充分条件成立,则相应的SQP算法具有2一一步超线性收敛性. 相似文献
11.
本文讨论不等式约束优化问题,给出一个信赖域方法与SQP方法相结合的新的可行算法,算法中采用了压缩技术,使得QP子问题产生的搜索方向尽可能为可行方向,并且采用了高阶校正的方法来克服算法产生的Maratos效应现象.在适当的条件下,证明了算法的全局收敛性和超线性收敛性.数值结果表明算法是有效的. 相似文献
12.
A Modified SQP Method and Its Global Convergence 总被引:6,自引:0,他引:6
Guanglu Zhou 《Journal of Global Optimization》1997,11(2):193-205
The sequential quadratic programming method developed by Wilson, Han andPowell may fail if the quadratic programming subproblems become infeasibleor if the associated sequence of search directions is unbounded. In [1], Hanand Burke give a modification to this method wherein the QP subproblem isaltered in a way which guarantees that the associated constraint region isnonempty and for which a robust convergence theory is established. In thispaper, we give a modification to the QP subproblem and provide a modifiedSQP method. Under some conditions, we prove that the algorithm eitherterminates at a Kuhn–Tucker point within finite steps or generates aninfinite sequence whose every cluster is a Kuhn–Tucker point.Finally, we give some numerical examples. 相似文献
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In this paper, a modified SQP method with nonmonotone line search technique is presented based on the modified quadratic subproblem proposed in Zhou (1997) and the nonmonotone line search technique. This algorithm starts from an arbitrary initial point, adjusts penalty parameter automatically and can overcome the Maratos effect. What is more, the subproblem is feasible at each iterate point. The global and local superlinear convergence properties are obtained under certain conditions. 相似文献
15.
The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization 总被引:3,自引:0,他引:3
Zengxin Wei Gaohang Yu Gonglin Yuan Zhigang Lian 《Computational Optimization and Applications》2004,29(3):315-332
The BFGS method is the most effective of the quasi-Newton methods for solving unconstrained optimization problems. Wei, Li, and Qi [16] have proposed some modified BFGS methods based on the new quasi-Newton equation B
k+1
s
k = y*
k
, where y*
k
is the sum of y
k and A
k
s
k, and A
k is some matrix. The average performance of Algorithm 4.3 in [16] is better than that of the BFGS method, but its superlinear convergence is still open. This article proves the superlinear convergence of Algorithm 4.3 under some suitable conditions. 相似文献
16.
A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization 总被引:2,自引:0,他引:2
Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising. 相似文献
17.
Jin-bao Jian Ran Quan Qing-jie Hu 《应用数学学报(英文版)》2007,23(3):395-410
In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming (SQP), a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming (QP) which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported. 相似文献
18.
Juliang Zhang+ 《计算数学(英文版)》2003,(2)
A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported. 相似文献
19.
一个修正HS共轭梯度法及其收敛性 总被引:2,自引:0,他引:2
It is well-known that the direction generated by Hestenes-Stiefel (HS) conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel (MHS) method is that the scalar βkH Sffikeeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods. 相似文献
20.
不等式约束优化一个具有超线性收敛的可行序列二次规划算法 总被引:2,自引:0,他引:2
建立了一个新的SQP算法,提出了一阶可行条件这一新概念.对已有SQP型算法进行改进,减少计算工作量,证明了算法具有全局收敛及超线性收敛性.数值实验表明算法是有效的. 相似文献