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- Fabian Bastin, Vincent Malmedy, Mélodie Mouffe, Philippe L. Toint, Dimitri Tomanos
- Math. Program.
- 2010

We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to… (More)

- L. Toint, Vincent Malmedy, Philippe L. Toint
- 2008

We consider Hessian approximation schemes for large-scale multilevel unconstrained optimization problems, which typically present a sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finitedifference methods and updating schemes based on the secant equation are presented… (More)

- Vincent Malmedy, Philippe L. Toint
- Comp. Opt. and Appl.
- 2011

We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finitedifference methods and updating… (More)

- Serge Gratton, Vincent Malmedy, Philippe L. Toint
- Comp. Opt. and Appl.
- 2012

- Serge Gratton, Vincent Malmedy, Philippe L. Toint
- Optimization Methods and Software
- 2015

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

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