Where Solving for Stationary Points by LCPs is Mixing Newton Iterates

A stationary point for a convex polyhedral set and a continuously differentiable function with positive semi-definite derivatives is computed by iteratively solving the linearized problem which is a linear complementarity problem (LCP). The procedure is shown to be a mixing of a finite number of Newton methods all converging to the same points, and consequently, to have convergence properties like Newton’s methods.