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Article Dans Une Revue Journal of Optimization Theory and Applications Année : 2017

A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization

Résumé

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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Dates et versions

hal-01710165 , version 1 (15-02-2018)

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Paul Armand, Riadh Omheni. A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization. Journal of Optimization Theory and Applications, 2017, 173 (2), pp.523-547. ⟨10.1007/s10957-017-1071-x⟩. ⟨hal-01710165⟩
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