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
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
Presolving in linear programming
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
Warm start of the primal-dual method applied in the cutting-plane scheme
Mathematical Programming: Series A and B
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Computational Experience with an Interior Point Cutting Plane Algorithm
SIAM Journal on Optimization
An Interior-Point Approach to Sensitivity Analysis in Degenerate Linear Programs
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
An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming
Mathematics of Operations Research
The integration of an interior-point cutting plane method within a branch-and-price algorithm
Mathematical Programming: Series A and B
An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems
Mathematics of Operations Research
Computational Optimization and Applications
Interior-point methods for nonconvex nonlinear programming: regularization and warmstarts
Computational Optimization and Applications
On Interior-Point Warmstarts for Linear and Combinatorial Optimization
SIAM Journal on Optimization
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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We implement several warm-start strategies in interior-point methods for linear programming (LP). We study the situation in which both the original LP instance and the perturbed one have exactly the same dimensions. We consider different types of perturbations of data components of the original instance and different sizes of each type of perturbation. We modify the state-of-the-art interior-point solver PCx in our implementation. We evaluate the effectiveness of each warm-start strategy based on the number of iterations and the computation time in comparison with "cold start" on the NETLIB test suite. Our experiments reveal that each of the warm-start strategies leads to a reduction in the number of interior-point iterations especially for smaller perturbations and for perturbations of fewer data components in comparison with cold start. On the other hand, only one of the warm-start strategies exhibits better performance than cold start in terms of computation time. Based on the insight gained from the computational results, we discuss several potential improvements to enhance the performances of such warm-start strategies.