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831.
We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based
technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions:
the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction.
A test based on the quadratic model of the objective function is used to select the most promising between the two search
directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly
rely on conjugacy conditions. An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization
is used with the approximate Newton step, while an Armijo type linesearch is used for the negative curvature direction. The
proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary conditions.
We carry out a significant numerical experience in order to test our proposal. 相似文献
832.
We present a new semi-local convergence theorem for the inexact Newton methods in the assumption that the derivative satisfies some kind of weak Lipschitz conditions. As special cases of our main result we re-obtain some well-known convergence theorems for Newton methods. 相似文献
833.
In this paper, we propose a new implementation of the Newton scheme of an approximate preconditioner for the reduced linear system. In the original Newton scheme, the trouble is that the computation cost of the matrix–matrix product is always so expensive. On the other hand, the proposed implementation computes the preconditioner implicitly and reduces the cost of constructing the preconditioner by using the matrix–vector product form. We also show that the proposed implementation is less expensive than computing the preconditioner in explicit form. 相似文献
834.
Runge-Kutta方法用于非线性方程求根 总被引:3,自引:0,他引:3
将Runge-Kutta方法用于非线性方程求根问题,给出二阶,三阶和四阶对应的三个新的方程求根公式,证明了它们至少三次收敛到单根,线性收敛到重根.文末给出数值试验,且与其它已知求根公式做了比较.结果表明此方法具有较好的优越性,它们丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值. 相似文献
835.
A new smoothing algorithm for the solution of nonlinear complementarity problems (NCP) is introduced in this paper. It is
based on semismooth equation reformulation of NCP by Fischer–Burmeister function and its related smooth approximation. In
each iteration the corresponding linear system is solved only approximately. Since inexact directions are not necessarily
descent, a nonmonotone technique is used for globalization procedure. Numerical results are also presented.
Research supported by Ministry of Science, Republic of Serbia, grant No. 144006. 相似文献
836.
Consider the problem of minimizing the sum of p-norms, where p is a fixed real number in the interval [1,2]. This nondifferentiable problem arises in many applications, including the VLSI
(very-large-scale-integration) layout problem, the facilities location problem and the Steiner minimum tree problem under
a given topology. In this paper, we establish the optimality conditions, duality and uniqueness results for the problem. We
then present a smoothing Newton method by the semismooth equations which are derived from the optimality conditions. The method
is globally and superlinearly convergent, and moreover, it is quadratically convergent when p∈[1,3/2]∪{2}. Particularly, the quadratic convergence is proved for the case wherep∈(1,3/2]∪{2} without requiring strict complementarity. Preliminary numerical results are reported, which indicate that the
method proposed is extremely promising.
The work was supported by the Starting-Up Foundation (B13-B6050640) of Guangdong Province. 相似文献
837.
N. N. Kalitkin I. P. Poshivailo 《Computational Mathematics and Mathematical Physics》2008,48(7):1113-1118
Newton’s method is most frequently used to find the roots of a nonlinear algebraic equation. The convergence domain of Newton’s method can be expanded by applying a generalization known as the continuous analogue of Newton’s method. For the classical and generalized Newton methods, an effective root-finding technique is proposed that simultaneously determines root multiplicity. Roots of high multiplicity (up to 10) can be calculated with a small error. The technique is illustrated using numerical examples. 相似文献
838.
M. Möller 《国际流体数值方法杂志》2007,55(7):611-635
The algebraic flux correction (AFC) paradigm is equipped with efficient solution strategies for implicit time‐stepping schemes. It is shown that Newton‐like techniques can be applied to the nonlinear systems of equations resulting from the application of high‐resolution flux limiting schemes. To this end, the Jacobian matrix is approximated by means of first‐ or second‐order finite differences. The edge‐based formulation of AFC schemes can be exploited to devise an efficient assembly procedure for the Jacobian. Each matrix entry is constructed from a differential and an average contribution edge by edge. The perturbation of solution values affects the nodal correction factors at neighbouring vertices so that the stencil for each individual node needs to be extended. Two alternative strategies for constructing the corresponding sparsity pattern of the resulting Jacobian are proposed. For nonlinear governing equations, the contribution to the Newton matrix which is associated with the discrete transport operator is approximated by means of divided differences and assembled edge by edge. Numerical examples for both linear and nonlinear benchmark problems are presented to illustrate the superiority of Newton methods as compared to the standard defect correction approach. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
839.
It is shown that the dispersion relation of heat waves along nanowires or thin layers could allow to compare two different definitions of nonequilibrium temperature, since thermal waves are predicted to propagate with different phase speed depending on the definition of nonequilibrium temperature being used. The difference is small, but it could be in principle measurable in nanosystems, as for instance nanowires and thin layers, in a given frequency range. Such an experiment could provide a deeper view on the problem of the definition of temperature in nonequilibrium situations. 相似文献
840.
Zhiyong Si Tong Zhang Kun Wang 《International Journal of Computational Fluid Dynamics》2013,27(3-4):135-141
In this article, a Newton iterative mixed finite element method is presented for solving the stationary conduction–convection problems in two dimensions. The stability and the errors generated by both partitioning the space and solving nonlinear equations are analysed, which show that our method is stable and has good precision. Finally, some numerical experiments are given to confirm its effect. 相似文献