Artículos de revistas
Proximal methods for nonlinear programming: double regularization and inexact subproblems
Fecha
2010Registro en:
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v.46, n.2, p.279-304, 2010
0926-6003
10.1007/s10589-009-9274-1
Autor
ECKSTEIN, Jonathan
SILVA, Paulo J. S.
Institución
Resumen
This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.