Abstract:
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.
