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1.
The iterations of the quasilinear technique, employed in nonlinear volterra integral equations, are expressed as linear integral equations. By using Collocation Method, the solutions of these linear equations are approximated. Combining this and iterations of the quasilinear technique yields an approximation solution for nonlinear integral equations. The convergence is considered and the examples confirm the accuracy of the solution.  相似文献   

2.
The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.  相似文献   

3.
The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. We use this technique to initial value problems of functional differential equations showing that corresponding linear iterations converge to the unique solution of our problem and this convergence is superlinear  相似文献   

4.
本文研究了求解多层线性规划问题的整体优化算法,利用流动等值面技术,证明了算法的有限终止性,并给出实际例子验证了算法的有效性.  相似文献   

5.
1.IntroductionInthispaper,weconsiderthefollowingoptimizationproblem(P):minf(x)(P)e.t.gi(x)~0(j=1,...,m,),gi(x)s0(j==m,+l,...,m),wherex~(xl,'5x.)"EE",f(x),gi(x)(j=1,',m)areallreaLvaluedsmoothfunctions.Inrecentyears)SequentialQuadraticProgramming(SoP)algorithmshavebeenex-tensivelyusedforthesolutionofsuchproblems,andtheyhavebeenwidelyinvestigatedbymanyauthors(see,e.g.[1-5]).AnattractivefeatureoftheSoPmethodisthat,undersomesuitableconditions,asuperlinearconvergencecanbeobtained,providedth…  相似文献   

6.
Numerical Algorithms - The Extrapolation Algorithm is a technique devised in 1962 for accelerating the rate of convergence of slowly converging Picard iterations for fixed point problems. Versions...  相似文献   

7.
In this paper, we address the primal-dual column generation technique, which relies on well-centred suboptimal solutions of the restricted master problems. We summarize new theoretical developments and present computational results for two classical combinatorial optimization problems, in which this technique has not been tested before. The results show that the primal-dual column generation technique usually leads to substantial reductions in the number of iterations and CPU time when compared to two other well-established approaches: the classical column generation technique and the analytic centre cutting plane method.  相似文献   

8.
A new technique for acceleration of convergence of static and dynamic iterations for systems of linear equations and systems of linear differential equations is proposed. This technique is based on splitting the matrix of the system in such a way that the resulting iteration matrix has a minimal spectral radius for linear systems and a minimal spectral radius for some value of a parameter in Laplace transform domain for linear differential systems.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

9.
Numerical Algorithms - Projection adjustment is a technique that improves the rate of convergence, as measured by the number of iterations needed to achieve a given level of performance, of the...  相似文献   

10.
In a wide range of applications it is required to compute the nearest correlation matrix in the Frobenius norm to a given symmetric but indefinite matrix. Of the available methods with guaranteed convergence to the unique solution of this problem the easiest to implement, and perhaps the most widely used, is the alternating projections method. However, the rate of convergence of this method is at best linear, and it can require a large number of iterations to converge to within a given tolerance. We show that Anderson acceleration, a technique for accelerating the convergence of fixed-point iterations, can be applied to the alternating projections method and that in practice it brings a significant reduction in both the number of iterations and the computation time. We also show that Anderson acceleration remains effective, and indeed can provide even greater improvements, when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. Alternating projections is a general method for finding a point in the intersection of several sets and ours appears to be the first demonstration that this class of methods can benefit from Anderson acceleration.  相似文献   

11.
《Optimization》2012,61(6):733-763
We present a non-monotone trust region algorithm for unconstrained optimization. Using the filter technique of Fletcher and Leyffer, we introduce a new filter acceptance criterion and use it to define reference iterations dynamically. In contrast with the early filter criteria, the new criterion ensures that the size of the filter is finite. We also show a correlation between problem dimension and the filter size. We prove the global convergence of the proposed algorithm to first- and second-order critical points under suitable assumptions. It is significant that the global convergence analysis does not require the common assumption of monotonicity of the sequence of objective function values in reference iterations, as assumed by the standard non-monotone trust region algorithms. Numerical experiments on the CUTEr problems indicate that the new algorithm is competitive compared to some representative non-monotone trust region algorithms.  相似文献   

12.
This article presents a numerical method for solving nonlinear mixed Volterra–Fredholm integral equations. The method combined with the noise terms phenomena may provide the exact solution by using two iterations only. Two numerical illustrations are given to show the pertinent features of the technique. The results reveal that the proposed method is very effective and simple.  相似文献   

13.
In this paper, we propose an interior-point algorithm for monotone linear complementarity problems. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full-Newton steps. Moreover, it is proven that the number of iterations of the algorithm coincides with the well-known best iteration bound for monotone linear complementarity problems.  相似文献   

14.
The optimal solutions of the restricted master problems typically leads to an unstable behavior of the standard column generation technique and, consequently, originates an unnecessarily large number of iterations of the method. To overcome this drawback, variations of the standard approach use interior points of the dual feasible set instead of optimal solutions. In this paper, we focus on a variation known as the primal–dual column generation technique which uses a primal–dual interior point method to obtain well-centered non-optimal solutions of the restricted master problems. We show that the method converges to an optimal solution of the master problem even though non-optimal solutions are used in the course of the procedure. Also, computational experiments are presented using linear-relaxed reformulations of three classical integer programming problems: the cutting stock problem, the vehicle routing problem with time windows, and the capacitated lot sizing problem with setup times. The numerical results indicate that the appropriate use of a primal–dual interior point method within the column generation technique contributes to a reduction of the number of iterations as well as the running times, on average. Furthermore, the results show that the larger the instance, the better the relative performance of the primal–dual column generation technique.  相似文献   

15.
AGENERALTECHNIQUEFORDEALINGWITHDEGENERACYINREDUCEDGRADIENTMETHODSFORLINEARLYCONSTRAINED NONLINEAR PROGRAMMINGHANJIYE(韩继业);HUX...  相似文献   

16.
The alternating direction method is one of the attractive approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iterations depends significantly on the penalty parameter for the system of linear constraint equations. While the penalty parameter is a constant in the original method, in this paper we present a modified alternating direction method that adjusts the penalty parameter per iteration based on the iterate message. Preliminary numerical tests show that the self-adaptive adjustment technique is effective in practice.  相似文献   

17.
In the context of the monotone Newton theorem (MNT) it has been conjectured that discretised Brown iterations converge at least as fast as discretised Newton iterations, because such is the case for analytic iterations. With easily verified hypotheses, it is proved here that Brown analytic iterations converge strictly faster than Newton ones. As a consequence, the same result holds for discretised iterations with conveniently small incremental steps. However, in the general context of the MNT, it may happen that Newton's discretised method converges faster than Brown's, but this situation can be remedied in many cases by conveniently shifting the initial value, so that those hypotheses ensuring the reverse are satisfied. Thus, a fairly effective solution is given to the problem stated initially.  相似文献   

18.
In this paper, an axiomatic definition of continuous iterations of a dynamical map is provided. From the axioms that define common properties of all continuous iterations, it will be demonstrated that continuous iterations that are also derivable must satisfy a certain nonlinear differential equation, herein referred as the “Equation of Derivable Continuous Iterations”. A general solution of this equation will be obtained by means of the Laplace transform and it will be shown that derivable continuous iterations of a map must have a certain functional form. A formula for analytically calculating derivable continuous iterations of maps with at least a fixed point is provided.  相似文献   

19.
In this work we study a class of secant-like iterations for solving nonlinear equations in Banach spaces. We consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz and Hölder continuous conditions. A semilocal convergence result is obtained for nondifferentiable operators. For that, we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution. Finally, we apply our results to the numerical solution of several examples.  相似文献   

20.
We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M-matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.  相似文献   

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