SIAM Journal on Control and Optimization
Mathematics of Operations Research
An OL(n3) potential reduction algorithm for linear programming
Mathematical Programming: Series A and B
A short-cut potential reduction algorithm for linear programming
Management Science
An active-set strategy in an interior point method for linear programming
Mathematical Programming: Series A and B
On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms
Mathematical Programming: Series A and B
A polynomial primal-dual Dikin-type algorithm for linear programming
Mathematics of Operations Research
Primal-dual interior-point methods
Primal-dual interior-point methods
Introduction to Linear Optimization
Introduction to Linear Optimization
Constraint Reduction for Linear Programs with Many Inequality Constraints
SIAM Journal on Optimization
On Mehrotra-Type Predictor-Corrector Algorithms
SIAM Journal on Optimization
Further development of multiple centrality correctors for interior point methods
Computational Optimization and Applications
Applied Numerical Mathematics
Matrix-free interior point method
Computational Optimization and Applications
Infeasible constraint-reduced interior-point methods for linear optimization
Optimization Methods & Software - Special issue in honour of Professor Florian A. Potra's 60th birthday
Designing Optimal Spectral Filters for Inverse Problems
SIAM Journal on Scientific Computing
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Consider linear programs in dual standard form with n constraints and m variables. When typical interior-point algorithms are used for the solution of such problems, updating the iterates, using direct methods for solving the linear systems and assuming a dense constraint matrix A, requires $\mathcal{O}(nm^{2})$ operations per iteration. When n驴m it is often the case that at each iteration most of the constraints are not very relevant for the construction of a good update and could be ignored to achieve computational savings. This idea was considered in the 1990s by Dantzig and Ye, Tone, Kaliski and Ye, den Hertog et al. and others. More recently, Tits et al. proposed a simple "constraint-reduction" scheme and proved global and local quadratic convergence for a dual-feasible primal-dual affine-scaling method modified according to that scheme. In the present work, similar convergence results are proved for a dual-feasible constraint-reduced variant of Mehrotra's predictor-corrector algorithm, under less restrictive nondegeneracy assumptions. These stronger results extend to primal-dual affine scaling as a limiting case. Promising numerical results are reported.As a special case, our analysis applies to standard (unreduced) primal-dual affine scaling. While we do not prove polynomial complexity, our algorithm allows for much larger steps than in previous convergence analyses of such algorithms.