A Concept for Global Optimization using the Function Imbedding Technique

Global optimal solutions for nonconvex problems are found by using the Function Imbedding Technique to imbed a nonconvex function into a higher dimensional convex function so that the original problem can be transformed into the problem of finding the mini-max solution of a related Lagrangian function. The Lagrangian function is chesen so that the associate dual cost function is concave, and so that the global optimal solution can be obtained from the saddle point of the Lagrangian, which can be found using ordinary numerical methods. A general theory is developed for determining when the duality gap vanishes.