Unified Interior Point Methodology For Canonical Duality In Global Optimization

We propose an interior point method to solve instances of the nonconvex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total complementarity function. We establish the global convergence result for the algorithm under mild assumptions. Our methodology is quite general and can be applied to several problemswhich dual has been formulated with canonical duality theory and shows the possibility of devising efficient interior points methods for nonconvex duality.