Distributed optimization has always been an active research area which receives extensive attention and interest. This trend has becoming increasingly obvious during the past decade, especially with the advent of ubiquitous multi-agent systems. In such a multi-agent system, there is no centralized controller and information exchange among users cannot be carried out in a systematic way. This feature makes it essential to develop distributed solution methods which require a limited level of coordination among users. Distributed solution methods can also be beneficial when there is a centralized controller, as they can make better use of problem structures and the convergence speed is usually much faster than centralized solvers.

In this thesis, we study some problems in financia...[ Read more ]

Distributed optimization has always been an active research area which receives extensive attention and interest. This trend has becoming increasingly obvious during the past decade, especially with the advent of ubiquitous multi-agent systems. In such a multi-agent system, there is no centralized controller and information exchange among users cannot be carried out in a systematic way. This feature makes it essential to develop distributed solution methods which require a limited level of coordination among users. Distributed solution methods can also be beneficial when there is a centralized controller, as they can make better use of problem structures and the convergence speed is usually much faster than centralized solvers.

In this thesis, we study some problems in financial engineering, signal processing, and communication systems where distributed optimization plays a role. We first study the multi-portfolio optimization problem using a game-theoretical approach. Distributed optimization is used to efficiently compute the optimal portfolios. Then, we study resource allocation problems in cognitive radio systems, and propose two complementary solutions together with distributed algorithms which can be implemented with a limited level of coordination among users. Finally, we propose a distributed best-response algorithm for a general class of nonconvex stochastic optimization problems. These distributed algorithms are able to exploit the problem structures better than state-of-the-art gradient methods and are thus expected to converge faster.