Consider the generalized inequality
, where g is a mapping between normed linar spaces and
denotes the partial order induced by a closed convex cone K. The authors turn to study the global minimization of the functional
and give a new algorithm based on the Gauss- Newton approach. The algorithm replaces directional derivatives
and avoids the difficulties of the subgradient approach. The authors show also the convergence of this algorithm. Their perspective is a more geometric one, thereby eliminating the dependence on polyhedrality and finite dimensionality.