Interior Point Methods for Second-Order Cone Programming and OR Applications
Computational Optimization and Applications
Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming
Computational Optimization and Applications
The Q method for second order cone programming
Computers and Operations Research
On the convergence of an inexact primal-dual interior point method for linear programming
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Local path-following property of inexact interior methods in nonlinear programming
Computational Optimization and Applications
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We present a convergence analysis for a class of inexact infeasible-interior-point methods for solving linear programs. The main feature of inexact methods is that the linear systems defining the search direction at each interior-point iteration need not be solved to high accuracy. More precisely, we allow that these linear systems are only solved to a moderate accuracy in the residual, but no assumptions are made on the accuracy of the search direction in the search space. In particular, our analysis does not require that feasibility is maintained even if the initial iterate happened to be a feasible solution of the linear program. We also present a few numerical examples to illustrate the effect of using inexact search directions on the number of interior-point iterations.