nearly exact method – Optimization Online

A practical method for solving large-scale TRS

Published: 2009/03/07, Updated: 2010/05/16

Constrained Nonlinear Optimization, Nonlinear Optimization, Quadratic Programming eigenvalues, l-bfgs method, large-scale optimization, nearly exact method, negative curvature direction, trust-region methods

We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study in concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Mor\'{e}-Sorensen method that exploits the eigenstructure of … Read more

A modified nearly exact method for solving low-rank trust region subproblem

Published: 2004/05/31, Updated: 2004/12/12

Zhaosong Lu

Renato D.C. Monteiro

Nonlinear Optimization large-scale optimization, limited memory bfgs method, nearly exact method, sherman-morrison-woodbury formula, trust-region methods

In this paper we present a modified nearly exact (MNE) method for solving low-rank trust region (LRTR) subproblem. The LRTR subproblem is to minimize a quadratic function, whose Hessian is a positive diagonal matrix plus explicit low-rank update, subject to a Dikin-type ellipsoidal constraint, whose scaling matrix is positive definite and has the similar structure … Read more