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1.
Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints 总被引:6,自引:0,他引:6
In Ref. 1, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was proposed. At each iteration, this new algorithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of computation required for existing SQP algorithms. Moreover, unlike the quadratic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvable. In Ref. 2, it is shown that the new algorithm can also be used to deal with nonlinear optimization problems having both equality and inequality constraints, by solving an auxiliary problem. But the algorithm of Ref. 2 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve the work of Ref. 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcoming the aforementioned shortcomings. Some numerical results are also reported. 相似文献
2.
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
3.
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
4.
In this paper, the feasible type SQP method is improved. A new SQP algorithm is presented to solve the nonlinear inequality constrained optimization. As compared with the existing SQP methods, per single iteration, in order to obtain the search direction, it is only necessary to solve equality constrained quadratic programming subproblems and systems of linear equations. Under some suitable conditions, the global and superlinear convergence can be induced. 相似文献
5.
In this paper, a new SQP algorithm is presented to solve the general nonlinear programs with mixed equality and inequality constraints. Quoted from P. Spellucci (see [9]), this method maybe be named sequential equality constrained quadratic programming (SECQP) algorithm. Per single iteration, based on an active set strategy ( see [9]), this SECQP algorithm requires only to solve equality constrained quadratic programming subproblems or system of linear equations. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. 相似文献
6.
In this paper,a new globally convergent algorithm for nonlinear optimization prablems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per itera-tion. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i. e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic sub-problem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems pe 相似文献
7.
基于乘子交替方向法(ADMM)和序列二次规划(SQP)方法思想, 致力于研究线 性约束两分块非凸优化的新型高效算法. 首先, 以SQP思想为主线, 在其二次规划(QP)子问题的求解中引入ADMM思想, 将QP分解为两个相互独立的小规模QP求解. 其次, 借助增广拉格朗日函数和Armijo线搜索产生原始变量新迭代点. 最后, 以显式解析式更新对偶变量. 因此, 构建了一个新型ADMM-SQP算法. 在较弱条件下, 分析了算法通常意义下的全局收敛性, 并对算法进行了初步的数值试验. 相似文献
8.
A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints 总被引:1,自引:0,他引:1
The relationship between the mathematical program with linear complementarity constraints (MPLCC) and its inequality relaxation
is studied. Based on this relationship, a new sequential quadratic programming (SQP) method is presented for solving the MPLCC.
A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global
convergence results are derived without assuming the linear independence constraint qualification for MPEC, the nondegeneracy
condition, and any feasibility condition of the quadratic programming subproblems. Preliminary numerical results are reported.
Research is partially supported by Singapore-MIT Alliance and School of Business, National University of Singapore. 相似文献
9.
针对约束块可分的最优化问题,引入序列线性方程组方法和有效集策略,提出了一个求解约束块可分优化问题的QP-free型并行变量分配(PVD)算法.算法中用三个系数具有对称结构的线性方程组来代替PVD算法中的二次规划问题以求解线搜索方向,避免了约束不相容,减小了计算量.并且算法不要求约束是凸的.最后证明了QP-free型PVD算法的全局收敛性. 相似文献
10.
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
11.
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
12.
C. Ling L. Q. Qi G. L. Zhou S. Y. Wu 《Journal of Optimization Theory and Applications》2006,129(1):147-164
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth
nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the
integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome
this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth
nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always
feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are
given.
Communicated by F. Giannessi
His work was supported by the Hong Kong Research Grant Council
His work was supported by the Australian Research Council. 相似文献
13.
This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic
programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm
proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998),
5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration,
one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size.
Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict
complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence.
Some preliminary numerical results are reported. 相似文献
14.
JIANJINBAO 《高校应用数学学报(英文版)》1997,12(3):343-354
In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlineer equality and inequality Constraints, Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn‘t solve anyquadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algoritbh satisfy all inequity constraints and its step-length is computed by the straight line search,The algorithm is proved to possesa global and auperlinear convergence. 相似文献
15.
16.
In this article, unconstrained minimax problems are discussed, and a sequential quadratic programming (SQP) algorithm with a new nonmonotone linesearch is presented. At each iteration, a search direction of descent is obtained by solving a quadratic programming (QP). To circumvent the Maratos effect, a high-order correction direction is achieved by solving another QP and a new nonmonotone linesearch is performed. Under reasonable conditions, the global convergence and the rate of superlinear convergence are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. 相似文献
17.
Efficient Sequential Quadratic Programming Implementations for Equality-Constrained Discrete-Time Optimal Control 总被引:1,自引:0,他引:1
Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N
3. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction. 相似文献
18.
19.
Jin-bao Jian Xiao-yan Ke Hai-yan Zheng Chun-ming Tang 《Journal of Computational and Applied Mathematics》2009
Based on the ideas of norm-relaxed sequential quadratic programming (SQP) method and the strongly sub-feasible direction method, we propose a new SQP algorithm for the solution of nonlinear inequality constrained optimization. Unlike the previous work, at each iteration, the norm-relaxed quadratic programming subproblem (NRQPS) in our algorithm only consists of the constraints corresponding to an estimate of the active set, and the high-order correction direction (used to avoid the Maratos effect) is obtained by solving a system of linear equations (SLE) which also only consists of such a subset of constraints and gradients. Moreover, the line search technique can effectively combine the initialization process with the optimization process, and therefore (if the starting point is not feasible) the iteration points always get into the feasible set after a finite number of iterations. The global convergence is proved under the Mangasarian–Fromovitz constraint qualification (MFCQ), and the superlinear convergence is obtained without assuming the strict complementarity. Finally, the numerical experiments show that the proposed algorithm is effective and promising for the test problems. 相似文献
20.
非线性不等式约束最优化一个超线性与二次收敛的强次可行方法 总被引:1,自引:0,他引:1
本文讨论非线性不等式约束最优化问题,借助于序列线性方程组技术和强次可行方法思想,建立了问题的一个初始点任意的快速收敛新算法.在每次迭代中,算法只需解一个结构简单的线性方程组.算法的初始迭代点不仅可以是任意的,而且不使用罚函数和罚参数,在迭代过程中,迭代点列的可行性单调不减.在相对弱的假设下,算法具有较好的收敛性和收敛速度,即具有整体与强收敛性,超线性与二次收敛性.文中最后给出一些数值试验结果. 相似文献