THESIS
2013
xviii, 102 pages : illustrations ; 30 cm
Abstract
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...[
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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.
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