A sufficient and necessary condition for non-convex constrained optimization

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