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We propose to solve large instances of the non-convex optimization problemsreformulated with canonical duality theory. To this aim we propose an interiorpoint potential reduction algorithm based on the solution of the primal-dualtotal complementarity (Lagrange) function. We establish the global convergenceresult for the algorithm under mild assumptions and demonstrate the method oninstances of the Sensor Network Localization problem. Our numerical results arepromising and show the possibility of devising efficient interior pointsmethods for non-convex duality.

A Potential Reduction Method for Canonical Duality, with an Application to the Sensor Network Localization Problem