Optimization Online


A 2-BFGS updating in a trust region framework

Marianna S. Apostolopoulou (msa***at***math.upatras.gr)
Dimitris G. Sotiropoulos (dgs***at***ionio.gr)
Panagiotis Pintelas (pintelas***at***math.upatras.gr)

Abstract: We present a new matrix-free method for the trust region subproblem, assuming that the approximate Hessian is updated by the limited memory BFGS formula with m = 2. The resulting updating scheme, called 2-BFGS, give us the ability to determine via simple formulas the eigenvalues of the resulting approximation. Thus, at each iteration, we can construct a positive definite matrix whose inverse can be expressed analytically, without using factorization. Consequently, a direction of negative curvature can be computed immediately by applying the inverse power method. Thus, the computation of the trial step can be obtained by performing a sequence of inner products and vector summations. Furthermore, it immediately follows that the strong convergence properties of trust region methods are preserved. Numerical results are also presented.

Keywords: large scale problems, unconstrained optimization, trust-region subproblem, limited memory BFGS, eigenvalues

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report No. TR07-01, University of Patras, Department of Mathematics, June 2007. Appeared in: Optimization Methods and Software http://dx.doi.org/10.1080/10556780802413579

Download: [PDF]

Entry Submitted: 07/15/2007
Entry Accepted: 07/15/2007
Entry Last Modified: 09/20/2008

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society