The Mathematical Institute, University of Oxford, Eprints Archive

A Primal-Dual Augmented Lagrangian

Gill, Philip E. and Robinson, Daniel P. (2008) A Primal-Dual Augmented Lagrangian. Technical Report. Unspecified. (Submitted)



Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1075
Deposited By: Lotti Ekert
Deposited On:06 May 2011 07:23
Last Modified:29 May 2015 18:46

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