共查询到20条相似文献,搜索用时 78 毫秒
1.
In this paper, a new sequential penalty algorithm, based on the Linfin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. 相似文献
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非线性约束条件下一个超线性收敛的可行方法 总被引:3,自引:0,他引:3
在本文中,我们对非线性不等式约束条件下的非线性优化问题给出了一个新的SQP类可行方法.此算法不但结构简单、易于计算,并且在适当的假设条件下,我们证明了算法具有全局收敛性及超线性收敛性 相似文献
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Jin-Bao Jian Qing-Jie Hu Hai-Yan Zheng 《Numerical Functional Analysis & Optimization》2013,34(3-4):376-409
Combining the ideas of generalized projection and the strongly subfeasible sequential quadratic programming (SQP) method, we present a new strongly subfeasible SQP algorithm for nonlinearly inequality-constrained optimization problems. The algorithm, in which a new unified step-length search of Armijo type is introduced, starting from an arbitrary initial point, produces a feasible point after a finite number of iterations and from then on becomes a feasible descent SQP algorithm. At each iteration, only one quadratic program needs to be solved, and two correctional directions are obtained simply by explicit formulas that contain the same inverse matrix. Furthermore, the global and superlinear convergence results are proved under mild assumptions without strict complementarity conditions. Finally, some preliminary numerical results show that the proposed algorithm is stable and promising. 相似文献
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One of the most interesting topics related to sequential quadratic programming algorithms is how to guarantee the consistence
of all quadratic programming subproblems. In this decade, much work trying to change the form of constraints to obtain the
consistence of the subproblems has been done. The method proposed by De O. Pantoja J.F. A. and coworkers solves the consistent
problem of SQP method, and is the best to the authors’ knowledge. However, the scale and complexity of the subproblems in
De O. Pantoja’s work will be increased greatly since all equality constraints have to be changed into absolute form. A new
sequential quadratic programming type algorithm is presented by means of a special ε-active set scheme and a special penalty
function. Subproblems of the new algorithm are all consistent, and the form of constraints of the subproblems is as simple
as one of the general SQP type algorithms. It can be proved that the new method keeps global convergence and Local superlinear
convergence.
Project partly supported by the National Natural Science Foundation of China. 相似文献
7.
SEQUENTIAL SYSTEMS OF LINEAR EQUATIONS ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS-INEQUALITY CONSTRAINED PROBLEMS 总被引:3,自引:0,他引:3
Zi-you Gao 《计算数学(英文版)》2002,(3)
AbstractIn this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported. 相似文献
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In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of the sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising. 相似文献
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An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point 总被引:6,自引:0,他引:6
For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search
direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this
algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related
quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using ε-active set procedure
with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general
nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems
of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence.
To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.
Project partly supported by the National Natural Science Foundation of China and Tianyuan Foundation of China. 相似文献
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XiuNaihua 《高校应用数学学报(英文版)》2000,15(4):433-442
In this paper, the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints ,and a SQP algorithm for this reformulation based on a damped Gauss-Newton type method is presented. It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity. 相似文献
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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
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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
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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
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Qing-jie Hu Yu Chen Nei-ping Chen Xue-quan Li 《Journal of Mathematical Analysis and Applications》2009,360(1):211-222
In this paper, a modified nonmonotone line search SQP algorithm for nonlinear minimax problems is presented. During each iteration of the proposed algorithm, a main search direction is obtained by solving a reduced quadratic program (QP). In order to avoid the Maratos effect, a correction direction is generated by solving the reduced system of linear equations. Under mild conditions, the global and superlinear convergence can be achieved. Finally, some preliminary numerical results are reported. 相似文献
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On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization
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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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提出一种改进的求解极小极大问题的信赖域滤子方法,利用SQP子问题来求一个试探步,尾服用滤子来衡量是否接受试探步,避免了罚函数的使用;并且借用已有文献的思想, 使用了Lagrange函数作为效益函数和非单调技术,在适当的条件下,分析了算法的全局和局部收敛性,并进行了数值实验. 相似文献
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Wenjuan Xue & Weiai Liu 《计算数学(英文版)》2020,38(5):683-704
We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrained
optimization problems. In our proposed algorithm, the constraints are partitioned into
several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part
of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The
other is that feasibility restoration phases are unnecessary because a consistent quadratic
programming subproblem is used. We prove that our algorithm is globally convergent to
KKT points under the constant positive generators (CPG) condition which is weaker than
the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant
positive linear dependence (CPLD). Numerical results are presented to show the efficiency
of the algorithm. 相似文献
19.
《Optimization》2012,61(1):23-38
Based on a smoothing approximation of a lower order penalty function and following Facchinei's method of dealing with the inconsistency of subproblems in SQP methods, we present a new robust SQP algorithm for solving a nonlinear constrained optimization problem. The proposed algorithm incorporates automatic adjustment rules for the choice of parameters. Under a new regularity condition at infeasible points, the algorithm is proved to be globally convergent. 相似文献
20.
An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions. 相似文献