A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization

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 introd...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 173; no. 2; pp. 523 - 547
Main Authors: Armand, Paul, Omheni, Riadh
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2017
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Estimates
Globalization
Jacobians
Lagrange multiplier
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Nonlinearity
Operations Research/Decision Theory
Optimization
Optimization and Control
Parameter estimation
Parameters
Quadratic programming
Studies
Theory of Computation
Primal–dual methods
90C51
65K05
90C30
Nonlinear optimization
Augmented Lagrangian
90C06
Interior-point methods
49M15
Constrained optimization
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1071-x