A hybrid of adjustable trust-region and nonmonotone algorithms for unconstrained optimization (original) (raw)
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RAL-TR-2004-009 A filter-trust-region method for unconstrained optimization
A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer and Toint (SIAM J. Optim., to appear, 2004) for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algorithm is shown to be globally convergent to at least one second-order critical point, and numerical experiments indicate that it is very competitive with more classical trust-region algorithms. 1 Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK. Email: n.gould@rl.ac.uk 2 Current reports available from “http://www.numerical.rl.ac.uk/reports/reports.shtml”. 3 This work was supported by the EPSRC grant GR/S42170 4 Department of Mathematics, Facultés Universitaires ND de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, EU....