A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B - Special issue on interior point methods for linear programming: theory and practice
Solving combinatorial optimization problems using Karmakar's algorithm
Mathematical Programming: Series A and B
Modified barrier functions (theory and methods)
Mathematical Programming: Series A and B
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
A primal-dual infeasible-interior-point algorithm for linear programming
Mathematical Programming: Series A and B
A new polynomial time method for a linear complementarity problem
Mathematical Programming: Series A and B
Polynomiality of infeasible-interior-point algorithms for linear programming
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Stability of Linear Equations Solvers in Interior-Point Methods
SIAM Journal on Matrix Analysis and Applications
Stability of Augmented System Factorizations in Interior-Point Methods
SIAM Journal on Matrix Analysis and Applications
Primal-dual interior-point methods
Primal-dual interior-point methods
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Warm start of the primal-dual method applied in the cutting-plane scheme
Mathematical Programming: Series A and B
Computational Experience with an Interior Point Cutting Plane Algorithm
SIAM Journal on Optimization
Multiple Cuts in the Analytic Center Cutting Plane Method
SIAM Journal on Optimization
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
Warm-Start Strategies in Interior-Point Methods for Linear Programming
SIAM Journal on Optimization
Warm Start and ε-Subgradients in a Cutting Plane Scheme
Computational Optimization and Applications
Reoptimization With the Primal-Dual Interior Point Method
SIAM Journal on Optimization
The Analytic Center Cutting Plane Method with Semidefinite Cuts
SIAM Journal on Optimization
Karmarkar's algorithm and combinatorial optimization problems
Karmarkar's algorithm and combinatorial optimization problems
The integration of an interior-point cutting plane method within a branch-and-price algorithm
Mathematical Programming: Series A and B
Computational Optimization and Applications
On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization
SIAM Journal on Optimization
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton steps
Optimization Methods & Software
Computational Optimization and Applications
A New Unblocking Technique to Warmstart Interior Point Methods Based on Sensitivity Analysis
SIAM Journal on Optimization
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Despite the many advantages of interior-point algorithms over active-set methods for linear optimization, one of the remaining practical challenges is their current limitation to efficiently solve series of related problems by an effective warmstarting strategy. As a remedy, in this paper we present a new infeasible-interior-point approach to quickly reoptimize an initial problem instance after data perturbations, or a new linear programming relaxation after adding cutting planes for discrete or combinatorial problems. Based on the detailed complexity analysis of the underlying algorithm, we perform a comparative analysis to coldstart initialization schemes and present encouraging computational results with iteration savings of around 50% on average for perturbations of the Netlib linear programs (LPs) and successive linear programming relaxations of max-cut and the traveling salesman problem.