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Now showing items 1-10 of 13

#### Linear programming via a quadratic penalty function

(Physica - Verlag, 1996)

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 ...

#### Piecewise-linear pathways to the optimal solution set in linear programming

(Kluwer Academic Publishers - Plenum Publishers, 1997)

This paper takes a fresh look at the application of quadratic penalty functions to linear programming. Recently, Madsen et al. (Ref. 1) described a continuation algorithm for linear programming based on smoothing a dual ...

#### Bound constrained quadratic programming via piecewise quadratic functions

(Springer-Verlag, 1999)

We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. ...

#### ℓ1 solution of linear inequalities

(Oxford University Press, 1999)

The numerical solution of a possibly inconsistent system of linear inequalities in the ℓ1 sense is considered. The non-differentiable ℓ1 norm minimization problem is approximated by a piecewise quadratic Huber smooth ...

#### Newton's method for linear inequality systems

(Elsevier, 1998)

We describe a modified Newton type algorithm for the solution of linear inequality systems in the sense of minimizing the ℓ2 norm of infeasibilities. Finite termination is proved, and numerical results are given. © 1998 ...

#### On Newton's method for Huber's robust M-estimation problems in linear regression

(Springer Netherlands, 1998)

The Newton method of Madsen and Nielsen (1990) for computing Huber's robust M-estimate in linear regression is considered. The original method was proved to converge finitely for full rank problems under some additional ...

#### A penalty continuation method for the ℓ∞ solution of overdetermined linear systems

(Springer Netherlands, 1998)

A new algorithm for the ℓ∞ solution of overdetermined linear systems is given. The algorithm is based on the application of quadratic penalty functions to a primal linear programming formulation of the ℓ∞ problem. The ...

#### New characterizations of ℓ1 solutions to overdetermined systems of linear equations

(Elsevier, 1994)

New characterizations of the ℓ1 solutions to overdetermined system of linear equations are given. The first is a polyhedral characterization of the solution set in terms of a special sign vector using a simple property of ...

#### A new finite continuation algorithm for linear programming

(Society for Industrial and Applied Mathematics, 1996)

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 ...

#### A characterization of the optimal set of linear programs based on the augmented lagrangian

(Taylor & Francis, 1999)

It is proved that in a certain neighborhood of the optimal set of multipliers, the set of minimizers of the augmented lagrangian nmction generates a new characterization of the optimal solution set of the linear program.