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A multilevel algorithm for solving the trust-region subproblem

Philippe L. Toint (philippe.toint***at***fundp.ac.be)
Dimitri Tomanos (dimitri.tomanos***at***fundp.ac.be)
Melissa Weber-Mendonca (melissa.weber***at***fundp.ac.be)

Abstract: 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 considered at the highest level (corresponding to the finest discretization), but information on the problem curvature at lower levels is exploited for improved efficiency. The algorithm is inspired by the method of More-Sorensen (1979), for which two different multilevel variants will be analyzed. Some preliminary numerical comparisons are also presented.

Keywords: nonlinear optimization, partial differential equations, multigrid, trust regions

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Infinite Dimensional Optimization (Other )

Category 3: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: OMS, to appear

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Entry Submitted: 10/01/2007
Entry Accepted: 10/01/2007
Entry Last Modified: 02/20/2009

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