Dipartimento di Ingegneria informatica, automatica e gestionale

In this talk we will explain the basis of the Canonical Duality Theory, starting from the concept of “transform” largely used in mathematics. Canonical Duality Theory is a potentially powerful methodology, which can be used to model complex systems and to reformulate a non-convex optimization in order to make simpler finding its global soultion.We will analyze the steps necessary to realize a canonical dual transformation of a general non-convex optimization problem. The obtained dual problem is canonical in respect to the primal in the sense that there is no duality gap. We will also describe the properties of the dual formulation and enunciate the “Triality Theory Theorem“ for the classification of the local and global extrema of general non-convex optimization problems.We will conclude giving also some important warnings and suggestions on the Canonical Duality Theory when it is applied to practical optimization problems.