A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization

Paul Armand () and Riadh Omheni ()
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Paul Armand: University of Limoges
Riadh Omheni: SAS Institute Inc.

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 8, 523-547

Abstract: Abstract We present a primal–dual algorithm for solving a constrained optimization problem. This method is based on a Newtonian method applied to a sequence of perturbed KKT systems. These systems follow from a reformulation of the initial problem under the form of a sequence of penalized problems, by introducing an augmented Lagrangian for handling the equality constraints and a log-barrier penalty for the inequalities. We detail the updating rules for monitoring the different parameters (Lagrange multiplier estimate, quadratic penalty and log-barrier parameter), in order to get strong global convergence properties. We show that one advantage of this approach is that it introduces a natural regularization of the linear system to solve at each iteration, for the solution of a problem with a rank deficient Jacobian of constraints. The numerical experiments show the good practical performances of the proposed method especially for degenerate problems.

Keywords: Nonlinear optimization; Constrained optimization; Augmented Lagrangian; Primal–dual methods; Interior-point methods; 49M15; 65K05; 90C06; 90C30; 90C51 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-017-1071-x

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