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+m1 × {0}Rm2). 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.
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