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 ...

Let B and T be n x n real matrices and r and n-vector and consider the system u = BTu+r. A new sufficient condition is given for the existence of a solution and convergence of a monotone process to a solution. The monotone ...

A generalized linear complementarity problem which is equivalent to finding a root of a piecewise-linear system of equations is shown to be solvable if and only if a related linear programming problem is solvable. ...

A Newton algorithm for solving the problem minimize f(x) subject to g(x) - 0, where f:Rn - R and g:Rn - Rm is given for the case when g is concave. At each step a convex quadractic program with linear constraints is solved ...

It is shown that McCormick's second order sufficient optimality conditions are also necessary for a solution to a quadratic program to be locally unique and hence these conditions completely characterize a locally unique ...