Variations on variable-metric methods. (With discussion)

On Variable - Metric Methods for Sparse Hessians

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...

Variable Metric Conjugate Gradient Methods

A family of variable metric proximal methods

We consider conceptual optimization methods combining two ideas: the Moreau-Yosida regularization in convex analysis, and quasi-Newton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasi-Newton updates of the o...

Splitting Methods with Variable Metric for K L Functions

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the KurdykaLojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward met...

Computational experience with improved variable metric methods for unconstrained minimization

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