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排序方式: 共有144条查询结果,搜索用时 31 毫秒
51.
This paper discusses the application of the Lanczos process to the solution of large-scale trust-region subproblems. Techniques pioneered by Golub based on Gauss quadrature are applied to derive inexpensively computable upper and lower bounds for quantities of interest. These bounds help determine how many steps of the Lanczos process should be carried out. 相似文献
52.
J. M. Martínez E. A. Pilotta M. Raydan 《Journal of Optimization Theory and Applications》2005,125(3):629-651
Linearly constrained optimization problems with simple bounds are considered in the present work. First, a preconditioned spectral gradient method is defined for the case in which no simple bounds are present. This algorithm can be viewed as a quasi-Newton method in which the approximate Hessians satisfy a weak secant equation. The spectral choice of steplength is embedded into the Hessian approximation and the whole process is combined with a nonmonotone line search strategy. The simple bounds are then taken into account by placing them in an exponential penalty term that modifies the objective function. The exponential penalty scheme defines the outer iterations of the process. Each outer iteration involves the application of the previously defined preconditioned spectral gradient method for linear equality constrained problems. Therefore, an equality constrained convex quadratic programming problem needs to be solved at every inner iteration. The associated extended KKT matrix remains constant unless the process is reinitiated. In ordinary inner iterations, only the right-hand side of the KKT system changes. Therefore, suitable sparse factorization techniques can be applied and exploited effectively. Encouraging numerical experiments are presented.This research was supported by FAPESP Grant 2001-04597-4 and Grant 903724-6, FINEP and FAEP-UNICAMP, and the Scientific Computing Center of UCV. The authors thank two anonymous referees whose comments helped us to improve the final version of this paper. 相似文献
53.
This paper describes a class of optimization methods that interlace iterations of the limited memory BFGS method (L-BFGS) and a Hessian-free Newton method (HFN) in such a way that the information collected by one type of iteration improves the performance of the other. Curvature information about the objective function is stored in the form of a limited memory matrix, and plays the dual role of preconditioning the inner conjugate gradient iteration in the HFN method and of providing an initial matrix for L-BFGS iterations. The lengths of the L-BFGS and HFN cycles are adjusted dynamically during the course of the optimization. Numerical experiments indicate that the new algorithms are both effective and not sensitive to the choice of parameters. 相似文献
54.
Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are proved to exhibit the local and superlinear convergence. 相似文献
55.
56.
《Optimization》2012,61(10):1717-1727
ABSTRACTIn this paper, we present a class of approximating matrices as a function of a scalar parameter that includes the Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno methods as special cases. A powerful iterative descent method for finding a local minimum of a function of several variables is described. The new method maintains the positive definiteness of the approximating matrices. For a region in which the function depends quadratically on the variables, no more than n iterations are required, where n is the number of variables. A set of computational results that verifies the superiority of the new method are presented. 相似文献
57.
58.
Ge Xinsheng Zhang Qizhi Chen Li-Qun 《Acta Mechanica Solida Sinica》2006,19(4):334-340
An optimal motion planning scheme based on the quasi-Newton method is proposedfor a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporatethe control energy, the final state errors and the constraints on states. The motion planning fordetermining control inputs to minimize the cost functional is formulated as a nonlinear optimalcontrol problem. Using the control parametrization, one can transform the infinite dimensionaloptimal control problem to a finite dimensional one that is solved via the quasi-Newton methodsfor a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planningscheme was applied to a rigid spacecraft with two momentum wheels. The simulation results showthe effectiveness of the proposed optimal motion planning scheme. 相似文献
59.
This paper investigates quasi-Newton updates for equality-constrained optimization. Using a least-change argument we derive
a class of rank-3 updates to approximations of the one-sided projection of the Hessian of the Lagrangian which keeps the appropriate
part symmetric (and possibly positive definite). By imposing the usual assumptions we are able to prove 1-step superlinear
convergence for one of these updates. Encouraging numerical results and comparisons with other previously analyzed updates
are presented.
Received: May 3, 1999 / Accepted: January 28, 2000?Published online March 15, 2000 相似文献
60.