Variable Metric Method for Minimization

Variable Metric Method for Minimization

Variable metric method for minimization of partially separable nonsmooth functions

In this report, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new met...

Limited-memory projective variable metric methods for unconstrained minimization

A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various projections are used. Numerical experience is e...

Computational experience with improved variable metric methods for unconstrained minimization

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A Variable-Metric Method for Function Minimization Derived from Invariancy to Nonlinear Scaling

The effect of nonlinearly scaling the objective function on the variable-metric method is investigated, and Broyden's update is modified so that a property of invariancy to the scaling is satisfied. A new three-parameter class of updates is generated, and criteria for an optimal choice of the parameters are given, Numerical experiments compare the performance of a number of algorithms of the re...