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Stopping rules and backward error analysis for bound-constrained optimization

Serge Gratton(serge.gratton***at***enseeiht.fr)
Melodie Mouffe(mouffe***at***cerfacs.fr)
Philippe Toint(philippe.toint***at***fundp.ac.be)

Abstract: Termination criteria for the iterative solution of bound-constrained optimization problems are examined in the light of backward error analysis. It is shown that the problem of determining a suitable perturbation on the problem's data corresponding to the definition of the backward error is analytically solvable under mild assumptions. Moreover, a link between existing termination criteria and this solution is clarified, indicating that some standard measures of criticality may be interpreted in the sense of backward error analysis. The backward error problem is finally considered from the multicriteria optimization point of view and some numerical illustration is provided.

Keywords: Nonlinear optimization, bound constraints, stopping criterion, backward error, multicriteria optimization.

Category 1: Nonlinear Optimization (Bound-constrained Optimization )

Category 2: Optimization Software and Modeling Systems (Optimization Software Design Principles )

Citation: Report 09/13, Department of Mathematics, FUNDP-University of Namur, Namur, Belgium, 2009

Download: [PDF]

Entry Submitted: 10/15/2009
Entry Accepted: 10/15/2009
Entry Last Modified: 10/15/2009

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