Global Optimization under Nonlinear Constraints Based on Apollonius Fill

Making use of Apollonius Fill, an algorithm is presented, which is for finding solutions of global optimization problems nonlinearly constrained by a circular region in the plane. Using this algorithm, global optimum can be computed fast and precisely. We request no more than first order derivatives of objective functions for the optimization algorithm. If we do not care about the processing time taken, for any given objective function, the global optimum can be obtained as precisely as requested. The proof of convergence of this algorithm is also given in this paper. We use a few numerical examples to show that this algorithm is effective, reliable, and hence is valuable in practice.