Mathematical Programming: Series A and B
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Local Convergence of the Affine-Scaling Interior-Point Algorithm for Nonlinear Programming
Computational Optimization and Applications
Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming
SIAM Journal on Optimization
A Trust-Region Approach to Nonlinear Systems of Equalities and Inequalities
SIAM Journal on Optimization
Local Convergence of a Primal-Dual Method for Degenerate Nonlinear Programming
Computational Optimization and Applications
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
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In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints.It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the binding inequality constraints are concave. In general, the q-quadratic rate is achieved provided the step in the primal variables does not become asymptotically orthogonal to any of the gradients of the binding inequality constraints.Some preliminary numerical experience showed that the feasible method can be implemented in a relatively efficient way, requiring a reduced number of function and derivative evaluations. Moreover, the feasible method is competitive with the classical infeasible primal-dual interior-point method in terms of number of iterations and robustness.