Solving the quadratic trust-region subproblem in a low-memory BFGS framework
نویسندگان
چکیده
منابع مشابه
Solving the quadratic trust-region subproblem in a low-memory BFGS framework
We present a new matrix-free method for the large-scale trust-region subproblem, assuming that the approximate Hessian is updated by the L-BFGS formula with m = 1 or 2. We determine via simple formulas the eigenvalues of these matrices and, at each iteration, we construct a positive definite matrix whose inverse can be expressed analytically, without using factorization. Consequently, a directi...
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The limited memory BFGS method pioneered by Jorge Nocedal is usually implemented as a line search method where the search direction is computed from a BFGS approximation to the inverse of the Hessian. The advantage of inverse updating is that the search directions are obtained by a matrix–vector multiplication. In this paper it is observed that limited memory updates to the Hessian approximatio...
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We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is co...
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The state-of-the-art algorithms for solving the trust-region subproblem are based on an iterative process, involving solutions of many linear systems, eigenvalue problems, subspace optimization, or line search steps. A relatively underappreciated fact, due to Gander, Golub and von Matt in 1989, is that trust-region subproblems can be solved by one generalized eigenvalue problem, with no outer i...
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ژورنال
عنوان ژورنال: Optimization Methods and Software
سال: 2008
ISSN: 1055-6788,1029-4937
DOI: 10.1080/10556780802413579