Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization
Abstract
Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented- info:eu-repo/semantics/article
- info:eu-repo/semantics/publishedVersion
- nonlinear programming
- augmented Lagrangian methods
- box constraints
- quasi-Newton
- truncated-Newton
- BOUND-CONSTRAINED OPTIMIZATION
- LINEAR-DEPENDENCE CONDITION
- PROJECTED GRADIENT METHODS
- UNCONSTRAINED MINIMIZATION
- GUARANTEED DESCENT
- CONVEX-SETS
- ALGORITHM
- BARZILAI
- QUALIFICATION
- CONVERGENCE
- Operations Research & Management Science
- Mathematics, Applied