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171.
172.
We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary
equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional
equations. We prove the convergence and stability of the scheme in L
2 and C norms.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005. 相似文献
173.
174.
175.
176.
We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1. 相似文献
177.
映象方程多解问题的某些研究 总被引:1,自引:0,他引:1
本文用fp-同伦方法,在一定的技巧和变换的配合下,在紧性条件支持下,研究了赋范线性空间中一类集值映象方程的多解问题。还给出所得理论结果的一个应用。 相似文献
178.
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
179.
具有奇异值分解性质的代数 总被引:4,自引:0,他引:4
设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域. 相似文献
180.
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