Canonical duality for solving nonconvex and nonsmooth optimization problem

摘要

This paper presents an application of the canonical duality theory for solving a class of nonconvex and nonsmooth optimization problems. It is shown that by use of the canonical dual transformation, these difficult optimization problems in R~n can be converted into a one-dimensional canonical dual problems, which can be solved to obtain all extremal points. Both global and local extremality conditions can be identified by the triality theory. Applications are illustrated.