Browsing by Subject "Finite algorithms"

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    Finite computation of the ℓ 1estimator from Huber's M-estimator in linear regression
    (2004) Pınar, M. Ç.
    We review and extend previous work on the approximation of the linear ℓ 1 estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne, and Madsen and Nielsen. Although the Madsen-Nielsen algorithm is a promising one, it is guaranteed to terminate finitely under certain assumptions. We describe a variant of the Madsen-Nielsen algorithm to compute the ℓ 1 estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.
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    Linear programming via a quadratic penalty function
    (Physica - Verlag, 1996) Pınar, M. Ç.
    We use quadratic penalty functions along with some recent ideas from linear l1 estimation to arrive at a new characterization of primal optimal solutions in linear programs. The algorithmic implications of this analysis are studied, and a new, finite penalty algorithm for linear programming is designed. Preliminary computational results are presented.
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    A new finite continuation algorithm for linear programming
    (Society for Industrial and Applied Mathematics, 1996) Madsen, K.; Nielsen, H. B.; Pınar, M. Ç.
    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.