Convergence and Error Bound for Perturbation of Linear Programs
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
An L1 estimation algorithm with degeneracy and linear constraints
Computational Statistics & Data Analysis
A software package for sparse orthogonal factorization and updating
ACM Transactions on Mathematical Software (TOMS)
A direct orthogonal sparse static methodology for a finite continuation hybrid LP solver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth problems are solved by a Newton-type algorithm. Preliminary numerical results indicate that the new algorithm is promising.