A number of characterizations are given which are both necessary and sufficient for the uniqueness of a solution to a linear programming problem.

It is shown that the linear complementarity problem of finding an n-by-1 vector x such that Mx + q > 0, x > 0, and xT(Mx+q) = 0, where M is a given n-by-n real matrix and q is a given n-by-l vector, is solvable if and ...

By perturbing a linear program to a quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as successive over-relaxation (SOR) methods. This provides a solution to the ...

The objective function of any solvable linear program can be perturbed by a differentiable, convex or Lipschitz continuous function in such a way that (a) a solution of the original linear program is also a Karush-Kuhn-Tucker ...

It is shown that the linear complementarity problem of finding a z in Rn such that Mz + q > 0, z > 0 and zT (Mz+q) = 0 can be solved by a single linear program in some important special cases such as when M or its inverse ...

Two medical applications of linear programming are described in this paper. Specifically, linear programming-based machine learning techniques are used to increase the accuracy of objectivity of breast cancer diagnosis and ...

An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. This leads to the minimization of an unconstrained di erentiable convex ...

The multiple instance classification problem [6,2,12] is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite dimensional (noninteger) real space subject to linear and bilinear ...