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A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization. (English) Zbl 1370.49022
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.

##### MSC:
 49M15 Newton-type methods 65K05 Numerical mathematical programming methods 90C06 Large-scale problems in mathematical programming 90C30 Nonlinear programming 90C51 Interior-point methods
##### Software:
ALGENCAN; AMPL; COPS; CUTEr; ipfilter; Ipopt; KNITRO; LANCELOT; LOQO; MA57; PENNON; SifDec; SNOPT
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