A global quadratic algorithm for solving a system of mixed equalities and inequalities

A new algorithm is proposed which, under mild assumptions, generates a sequence{x_i} that starting at any point inRⁿ will converge to a setX defined by a mixed system of equations and inequalities. Any iteration of the algorithm requires the solution of a linear programming problem with relatively few constraints. By only assuming that the functions involved are continuously differentiable a superlinear rate of convergence is achieved. No convexity whatsoever is required by the algorithm.