Convergence property of a class of variable metric methods

New class of limited-memory variationally-derived variable metric methods

A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported.

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...

Variable Metric Conjugate Gradient Methods

A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions

We extend the general decomposition scheme of [32], which is based on the hybrid inexact proximal point method of [38], to allow the use of variable metric in subproblems, along the lines of [23]. We show that the new general scheme includes as special cases the splitting method for composite mappings [25] and the proximal alternating directions method [13, 17] (in addition to the decomposition...

review of radiographic methods in dental implantology

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