A Gauss-Newton Approach to Solving Generalized Inequalities

Source abstract

Generalized inequalities are systems of the form g(x) ≤ K 0, where g maps between normed linear spaces and “≤ K ” denotes the partial order induced by the closed convex cone K (e.g., K = R + m 1 × {0} R m 2 ). In this paper a Gauss-Newton type algorithm is presented for minimizing the distance function [Formula: see text] The technique globalizes the well-known Newton methods for solving generalized inequalities, and overcomes the difficulties associated with subgradient methods for the global minimization of ρ.