A new finite continuation algorithm for linear programming
Nielsen, H. B.
Pınar, M. Ç.
SIAM Journal on Optimization
1052-6234 (print)1095-7189 (online)
Society for Industrial and Applied Mathematics
600 - 616
MetadataShow full item record
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/49284
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 f\ 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.