A quasi-Newton modified LP-Newton method

Abstract

We consider a method to solve constrained system of nonlinear equations based on a modification of the Linear-Programming-Newton method and replacing the first-order information with a quasi-Newton secant update, providing a computationally simple method. The proposed strategy combines good properties of two methods: the least change secant update for unconstrained system of nonlinear equations with isolated solutions and the Linear-Programming-Newton for constrained nonlinear system of equations with possible nonisolated solutions. We analyse the local convergence of the proposed method under a standard error bound condition proving its linear convergence for nonisolated solutions. Numerical experiments were done in order to show the claimed convergence rate.