Philippe Toint - Academia.edu (original) (raw)
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Papers by Philippe Toint
SIAM Journal on Optimization, 1999
The approximate minimization of a quadratic function within an ellipsoidal trust region is an imp... more The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, the most widely-used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust-region boundary. In this paper, we investigate ways of continuing the process once the boundary has been encountered. The key is to observe that the trust-region problem within the currently generated Krylov subspace has very special structure which enables it to be solved very e ciently. We compare the new strategy with existing methods. The resulting software package is available as HSL VF05 within the Harwell Subroutine Library.
SIAM Journal on Optimization, 1999
The approximate minimization of a quadratic function within an ellipsoidal trust region is an imp... more The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, the most widely-used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust-region boundary. In this paper, we investigate ways of continuing the process once the boundary has been encountered. The key is to observe that the trust-region problem within the currently generated Krylov subspace has very special structure which enables it to be solved very e ciently. We compare the new strategy with existing methods. The resulting software package is available as HSL VF05 within the Harwell Subroutine Library.