Sufficient Fritz John optimality conditions

Abstract

The sufficient optimality conditions, of Fritz John type, given by Gulati for finite-dimensional nonlinear programming problems involving polyhedral cones, are extended to problems with arbitrary cones and spaces of arbitrary dimension, whether real or complex. Convexity restrictions on the function giving the equality constraint can be avoided by applying a modified notion of convexity to the other functions in the problem. This approach regards the problem as optimizing on a differentiable manifold, and transforms the problem to a locally equivalent one where the optimization is on a linear subspace.