Quasi-Newton updates with weighted secant equations

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. Citation Report naXys-09-2013, Namur Centre for Complex Systems, Unibersity of Namur, Namur (Belgium) Article Download View Quasi-Newton updates with weighted secant equations

Using approximate secant equations in limited memory methods for multilevel unconstrained optimization

The properties of multilevel optimization problems defined on a hierarchy of discretization grids can be used to define approximate secant equations, which describe the second-order behaviour of the objective function. Following earlier work by Gratton and Toint (2009), we introduce a quasi-Newton method (with a linesearch) and a nonlinear conjugate gradient method that both take … Read more

Approximating Hessians in multilevel unconstrained optimization

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 finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by … Read more

A Retrospective Trust-Region Method for Unconstrained Optimization

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 … Read more