A SUFFICIENT AND NECESSARY CONDITION FOR NONCONVEX CONSTRAINED OPTIMIZATION

The conventional Lagrangian approach to solving constrained optimizati on problems leads to optimality conditions which are either necessary, or sufficient? but not both unless the underlying cost and constraint functions are also convex. We introduce a new approach based on the T chebyshev norm. This leads to an optimality condition which is both su fficient and necessary, without any convexity assumption. This optimal ity condition can be used to devise a conceptually simple method for s olving nonconvex inequality constrained optimization problems.