A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization |
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Authors: | Paul Armand Riadh Omheni |
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Affiliation: | 1.XLIM Laboratory - UMR CNRS no 7252,University of Limoges,Limoges,France;2.Advanced Analytics Devision, Operations Research and Management Science R&D,SAS Institute Inc.,Brie-Comte-Robert,France |
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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. |
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