Iterative schemes for the least 2-norm solution of piecewise linear programs Original Research Article

Let f : Rn → (−∞, ∞] be a convex polyhedral function. We show how to find the normal minimizer of f and the associated Lagrange multipliers by computing x(ε) = arg minx f(x) + ε x2/2 approximately for a sequence of ε ↓ 0 via any relaxation method applied to the corresponding dual problems. Our schemes generalize those of Managasarian and De Leone for solving very large sparse linear programs.