Global Optimization of a General Class of Nonconvex Optimization Problems

Title: Global Optimization of a General Class of Nonconvex Optimization Problems

In this work, a general class of nonconvex optimization problems is considered that possesses: a separable objective function consisting of general nonconvex terms;  a single equality constraint requiring that a product of general nonconvex single variable functions is equal to a constant parameter, and upper and lower bounds on all optimization variables. This class of problems is shown to arise frequently in practice, especially during the optimization of serial systems.

The proposed solution method employs optimality properties of the considered optimization problem, in combination with interval analysis, to guarantee that upper and lower bounds converging to the problem's global optimum are identified for all optimization problem instances created by varying the equality constraint's constant parameter. 

The proposed method is illustrated on a number of case studies.