# On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems

@article{Zhang1993OnTS, title={On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems}, author={Yin Zhang and Richard A. Tapia and Florian A. Potra}, journal={SIAM J. Optim.}, year={1993}, volume={3}, pages={413-422} }

In this paper, the authors extend the Q-superlinear convergence theory recently developed by Zhang, Tapia, and Dennis for a class of interior-point linear programming algorithms to similar interior-point algorithms for quadratic programming and for linear complementarily problems. This unified approach consists of viewing all these algorithms as a damped Newton method applied to perturbations of a general problem. A set of sufficient conditions for these algorithms to achieve Q-superlinear…

## 41 Citations

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We consider an interior point algorithm for convex programming in which the steps are generated by using a primal-dual aane scaling technique. A \local" variant of the algorithm is shown to have…

A Positive Algorithm for the Nonlinear Complementarity Problem

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A new iterative method for solving the (nonmonotone) nonlinear complementarily problem (NCP), based on a generalized Gauss–Newton scheme applied to a constrained nonsmooth-equations formulation of the complementarilyproblem, is described and established.

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This paper proves by example that the existence of a strictly complementarity solution appears to be necessary to achieve superlinear convergence for the predictor—corrector algorithm for linear programming (LP), assuming only that a strictly complementary solution exists.

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- 1996

This work presents an iterative algorithm for solving a constrained system of equations and investigates its convergence properties, including specialization of the algorithm and its convergence analysis to complementarity problems of various kinds and the Karush-Kuhn-Tucker systems of variational inequalities.

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- 1995

An interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions is described, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent.

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- Mathematics
- 1991

In this note we consider a large step modiication of the Mizuno-Todd-Ye O(p nL) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modiied algorithm…

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- 2008

The algorithm uses quasi-Newton search direction, based on sub-gradient information, conditional on maximizers, and adopts semi-infinite programming iterations towards epi-convergence in the case of multiple maximizers.

A FIRST ORDER PREDICTOR-CORRECTOR INFEASIBLE INTERIOR POINT METHOD FOR SUFFICIENT LINEAR COMPLEMENTARITY PROBLEMS IN A WIDE AND SYMMETRIC NEIGHBORHOOD OF THE CENTRAL PATH †

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- 2009

A new predictor-corrector method for solving sufficient linear complementarity problems (LCP) with an infeasible starting point which converges Q-quadratically to zero for nondegenerate problems and a variant of the original algorithm which does not depend on κ.

Inexact SQP Interior Point Methods and Large Scale Optimal Control Problems

- Mathematics, Computer ScienceSIAM J. Control. Optim.
- 1996

Based on a reformulation as a mixed nonlinear complementarity problem, a measure of when to terminate the iterative quadratic program solver is given for the latter using an interior point algorithm.

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