Decrease of the Penalty Parameter in Differentiable Penalty Function Methods

Decrease of the Penalty Parameter in Differentiable Penalty Function Methods

We propose a simple modification to the differentiable penalty methods for solving nonlinear programming problems. This modification decreases the penalty parameter and the ill-conditioning of the penalty method and leads to a faster convergence to the optimal solution. We extend the modification to the augmented Lagrangian method and report some numerical results on several nonlinear programmi...

Differentiable Local Barrier-Penalty Paths

Perturbations of Karush-Kuhn-Tuckerconditions play an importantrole forprimaldual interior point methods. Beside the usual logarithmic barrier various further techniques of sequential unconstrained minimization are well known. However other than logarithmic embeddings are rarely studied in connection with Newton path-following methods. A key property that allows to extend the class of methods i...

Differentiable Local Barrier-penalty Paths Barrier-penalty Paths

Perturbations of Karush-Kuhn-Tucker conditions play an important role for primal-dual interior point methods. Beside the usual logarithmic barrier various further techniques of sequential unconstrained minimization are well known. However other than logarithmic embeddings are rarely studied in connection with Newton path-following methods. A key property that allows to extend the class of metho...

Automatic Decrease of the Penalty

This paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modiications to the standard outer loop which decreases the penalty parameter (typically dividing it by a constant). The procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on...

Simplified Variants of Penalty Function Methods