New Kuhn–Tucker sufficiency for global optimality via convexification

In this paper, we first establish that the Kuhn–Tucker necessary optimality condition is sufficient for global optimality of the class of convexifiable programming problems with bounds on variables for which a local minimizer is global. This result yields easily verifiable Kuhn–Tucker sufficient conditions for non-convex quadratic programs. We also present new conditions for a feasible point which satisfies the Kuhn–Tucker conditions to be a global minimizer of multi-extremal mathematical programming problems which may have local minimizers that are not global. In the multi-extremal case, the convexifiability of an augmented Lagrangian function plays a key role in deriving the result. As an application, we also derive sufficient optimality conditions for multi-extremal bivalent programming problems. Several examples are given to illustrate the significance of the results.