Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
نویسندگان
چکیده
منابع مشابه
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
Abstract. A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is recursive, leading to true multilevel/mult...
متن کاملOn the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear Mechanics
We prove new convergence results for a class of multiscale trust–region algorithms introduced by Gratton et al. in [GST06] to solve unconstrained minimization problems within the Euclidean space R. We will state less restrictive assumptions on the function which has to be minimized and on the iteratively computed trust–region corrections, which allow for proving first– and second–order converge...
متن کاملMultilevel Optimization Using Recursive Trust-Region Methods
Many large-scale finite-dimensional optimization problems arise from the discretization of infinite-dimensional problems, a primary example being optimal-control problems defined in terms of either ordinary or partial differential equations. While the direct solution of such problems for a discretization level yielding the desired accuracy is often possible using existing packages for large-sca...
متن کاملNonlinear Optimization: Trust Region Algorithms
In this paper, we review the trust region algorithms for nonlinear optimization. The philosophy and the fundamental ideas of trust region algorithms are discussed. Model algorithms for unconstrained optimization, constrained optimization, and nonsmooth optimization are given. Main techniques for global convergence and local superlinear convergence are analyzed.
متن کاملNumerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization
We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer and Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2008
ISSN: 1052-6234,1095-7189
DOI: 10.1137/050623012