Abstract
This paper presents an application of the canonical duality theory for box constrained nonconvex and nonsmooth optimization problems. By use of the canonical dual transformation method, which is developed recently, these very difficult constrained optimization problems inRncan be converted into the canonical dual problems, which can be solved by deterministic methods. The global and local extrema can be identified by the triality theory. Some examples are listed to illustrate the applications of the theory presented in the paper.
Highlights
The methods of solving nonconvex and nonsmooth optimization have been the topic of intense research during the last forty years
This nonzero duality gap shows that the Fenchel-Rockafellar duality theory and method can be used mainly in convex systems
A perfect dual problem is formulated, which is equivalent to the primal problem in the sense that they have the same set of critical points
Summary
The methods of solving nonconvex and nonsmooth optimization have been the topic of intense research during the last forty years. Ps(x), the Young-Fenchel inequality can lead to a weak duality relationship in general nonconvex systems: This nonzero duality gap shows that the Fenchel-Rockafellar duality theory and method can be used mainly in convex systems. The so-called canonical dual transformation method (without the duality gap) has been developed in general nonconvex systems [21] This method is a newly useful tool for optimal problem. We will present the application of the canonical dual transformation method for the solutions of the box constrained nonconvex and nonsmooth optimization problems (P) in Rn. a perfect dual problem is formulated, which is equivalent to the primal problem in the sense that they have the same set of critical points.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call