On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
A primal-dual interior point method whose running time depends only on the constraint matrix
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Convergence Conditions and Krylov Subspace---Based Corrections for Primal-Dual Interior-Point Method
SIAM Journal on Optimization
Mehrotra-type predictor-corrector algorithm revisited
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
A constraint-reduced variant of Mehrotra's predictor-corrector algorithm
Computational Optimization and Applications
Matrix-free interior point method
Computational Optimization and Applications
A Predictor-corrector algorithm with multiple corrections for convex quadratic programming
Computational Optimization and Applications
Mehrotra-type predictor-corrector algorithms for sufficient linear complementarity problem
Applied Numerical Mathematics
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of re-centering in the implementation of interior point methods. Second-order correctors, such as Mehrotra's predictor---corrector, can occasionally fail: we derive a remedy to such difficulties from a new interpretation of multiple centrality correctors. Through extensive numerical experience we show that the proposed centrality correcting scheme leads to noteworthy savings over second-order predictor---corrector technique and previous implementations of multiple centrality correctors.