By enabling the nodes or agents to solve small-sized subproblems achieve coordination, distributed algorithms are favored by many networked systems for efficient and scalable computation. While convex problems, substantial available, results more broad nonconvex counterparts extremely lacking. This paper develops a algorithm class of nonsmooth problems featured (i) objective formed both separat...

Abstract. This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials ...

In machine learning and optimization, one often wants to minimize a convex objective function F but can only evaluate a noisy approximation F̂ to it. Even though F is convex, the noise may render F̂ nonconvex, making the task of minimizing F intractable in general. As a consequence, several works in theoretical computer science, machine learning and optimization have focused on coming up with pol...

In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization...

In engineering design, an optimized solution often turns out to be suboptimal, when errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method, which ...