On the Minimum Norm Solution to Weber Problem

On the Minimum Norm Solution of Linear Programs1

On the Minimum Norm Solution of Linear Programs

This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this ...

On the Minimum Norm

This paper describes a new technique to nd the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Ne...

Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formul...

A Smoothing Technique for the Minimum Norm Solution of Absolute Value Equation

One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have infinitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. ...