%A O. L. Mangasarian
%T Regularized Linear Programs with Equilibrium Constraints
%D November 1997
%R 97-13
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
We consider an arbitrary linear program with equilibrium constraints (LPEC)
that may possibly be infeasible or have an unbounded objective function.
We regularize the LPEC by perturbing it in a minimal way so
that the regularized problem is solvable. We show that such
regularization leads to a problem that is guaranteed to have
a solution which is an exact solution to the original LPEC
if that problem is solvable, otherwise it is a residual-minimizing
approximate solution to the original LPEC. We propose a finite successive
linearization algorithm for the regularized problem
that terminates at point satisfying the minimum principle
necessary optimality condition for the problem.