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#### 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 finite continuation algorithm for bound constrained quadratic programming

(Society for Industrial and Applied Mathematics Publications, 1998)

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear ℓ1 minimization problem with quadratic terms. A smooth approximation to the linear ℓ1 function is used to obtain a parametric ...

#### 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. ...