Local convergence of interior-point algorithms for degenerate monotone LCP
Computational Optimization and Applications
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
On the convergence rate of Newton interior-point methods in the absence of strict complementarity
Computational Optimization and Applications
Mathematical Programming: Series A and B
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution
Computational Optimization and Applications
Stabilized Sequential Quadratic Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Superlinear Convergence of an Interior-Point Method Despite Dependent Constraints
Mathematics of Operations Research
Effects of Finite-Precision Arithmetic on Interior-Point Methods for Nonlinear Programming
SIAM Journal on Optimization
Local Convergence of a Primal-Dual Method for Degenerate Nonlinear Programming
Computational Optimization and Applications
A Primal-Dual Exterior Point Method for Nonlinear Optimization
SIAM Journal on Optimization
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Recently studies of numerical methods for degenerate nonlinear optimization problems have been attracted much attention. Several authors have discussed convergence properties without the linear independence constraint qualification and/or the strict complementarity condition. In this paper, we are concerned with quadratic convergence property of a primal-dual interior point method, in which Newton's method is applied to the barrier KKT conditions. We assume that the second order sufficient condition and the linear independence of gradients of equality constraints hold at the solution, and that there exists a solution that satisfies the strict complementarity condition, and that multiplier iterates generated by our method for inequality constraints are uniformly bounded, which relaxes the linear independence constraint qualification. Uniform boundedness of multiplier iterates is satisfied if the Mangasarian-Fromovitz constraint qualification is assumed, for example. By using the stability theorem by Hager and Gowda (1999), and Wright (2001), the distance from the current point to the solution set is related to the residual of the KKT conditions.By controlling a barrier parameter and adopting a suitable line search procedure, we prove the quadratic convergence of the proposed algorithm.