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1.
Based on a differentiable merit function proposed by Taji et al. in "Math. Prog. Stud., 58, 1993, 369-383", the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. 相似文献
2.
本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率. 相似文献
3.
本文考虑复合函数 F(x)=f(x)+h(c(x))最小化问题,给出了校正矩阵逼近 Langrangian 函数的“单边投影 Hessian”的 Broyden-类型方法;此方法是 Q-超线性收敛的.文中还叙述了两个校正算法,并且证明了在合理的条件下,这两种算法都具有局部的两步 Q-超线性收敛性. 相似文献
4.
In this article, we propose the Gauss-Newton methods via conjugate gradient path for solving nonlinear systems. By constructing and solving a linearized model of the nonlinear systems, we obtain the iterative direction by employing the conjugate gradient path. In successive iterations, the approximate Jacobian of the nonlinear systems is updated by a Broyden formula to construct the conjugate path. The global convergence and local superlinear convergence rate of the proposed algorithms are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithms. 相似文献
5.
A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO
Kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not
only used for determining the search directions but also for measuring the distance between the given iterate and the μ-center for the algorithms. In this paper we present a unified kernel function approach to primal-dual interior-point algorithms
for convex quadratic semidefinite optimization based on the Nesterov and Todd symmetrization scheme. The iteration bounds
for large- and small-update methods obtained are analogous to the linear optimization case. Moreover, this unifies the analysis
for linear, convex quadratic and semidefinite optimizations. 相似文献
6.
Mehrotra's predictor-corrector algorithm [3] is currently considered to be one of the most practically efficient interior-point methods for linear programming. Recently, Zhang and Zhang [18] studied the global convergence properties of the Mehrotra-type predictor-corrector approach and established polynomial complexity bounds for two interior-point algorithms that use the Mehrotra predictor-corrector approach. In this paper, we study the asymptotic convergence rate for the Mehrotra-type predictor-corrector interior-point algorithms. In particular, we construct an infeasible-interior-point algorithm based on the second algorithm proposed in [18] and show that while retaining a complexity bound ofO(n
1.5
t)-iterations, under certain conditions the algorithm also possesses aQ-subquadratic convergence, i.e., a convergence ofQ-order 2 with an unboundedQ-factor.Research supported in part by NSF DMS-9102761 and DOE DE-FG02-93ER25171. 相似文献
7.
A new filter-line-search algorithm for unconstrained nonlinear optimization problems is proposed. Based on the filter technique introduced by Fletcher and Leyffer (Math. Program. 91:239–269, 2002) it extends an existing technique of Wächter and Biegler (SIAM J. Comput. 16:1–31, 2005) for nonlinear equality constrained problem to the fully general unconstrained optimization problem. The proposed method, which differs from their approach, does not depend on any external restoration procedure. Global and local quadratic convergence is established under some reasonable conditions. The results of numerical experiments indicate that it is very competitive with the classical line search algorithm. 相似文献
8.
Fumin Yang Chikun Xiao Wanzhen Chen Zhongping Zhang Detong Tan Xiangdong Gong Juping Chen Huang Li Jianhua Zhang 《中国科学A辑(英文版)》1999,42(2):198-206
The first satellite laser ranging system for daylight tracking in China was set up at Shanghai Observatory, Chinese Academy
of Sciences. Both false alarm probability due to strong background noises and detection probability of the laser returns with
single photon level from satellite in daylight for our system are analysed. The system design and performance characteristics
of subsystems, adopted techniques and satellite ranging observations are given.
Project supported by the astronomical council of Chinese Academy of Sciences and the National Basic Research Project “Modern
Crustal Movement and Geodynamics Research”. 相似文献
9.
朱德通 《高校应用数学学报(英文版)》2004,19(3):311-326
A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed. In order to deal with large problems,a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem. The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint. Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems. By adopting the l1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill-conditioned cases. 相似文献
10.
In this paper, a truncated conjugate gradient method with an inexact Gauss-Newton technique is proposed for solving nonlinear systems.?The iterative direction is obtained by the conjugate gradient method solving the inexact Gauss-Newton equation.?Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithm. 相似文献