Journal of Optimization Theory and Applications
Convergence of a Class of Inexact Interior-Point Algorithms for Linear Programs
Mathematics of Operations Research
A survey of truncated-Newton methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Mathematical Programming: Series A and B
Inexact constraint preconditioners for linear systems arising in interior point methods
Computational Optimization and Applications
A local convergence property of primal-dual methods for nonlinear programming
Mathematical Programming: Series A and B
Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming
Computational Optimization and Applications
An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations
SIAM Journal on Scientific Computing
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We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of the original system. In case of an exact solution of the Newton system, it has been shown that the sequence of iterates is asymptotically tangent to the central path (Armand and Benoist in Math. Program. 115:199---222, 2008). The purpose of the present paper is to extend this result to an inexact solution of the Newton system. We give quite general conditions on the different parameters of the algorithm, so that this asymptotic property is satisfied. Some numerical tests are reported to illustrate our theoretical results.