This thesis studies mechanism design from an optimization perspective.
Our main contribution is to characterize fundamental structural properties of optimization problems arising
in mechanism design and to exploit them to design general frameworks and techniques for efficiently solving
the underlying problems. Not only do our characterizations allow for efficient computation, they also reveal
qualitative characteristics of optimal mechanisms which are important even from a non-computational
standpoint. Furthermore, most of our techniques are widely applicable to optimization problems outside of
mechanism design such as online algorithms or stochastic optimization.
Our frameworks can be summarized as follows. When the input to an optimization problem (e.g., a mechanism
design problem) comes from independent sources (e.g., independent agents), the complexity of the problem can
be exponentially reduced by (i) decomposing the problem into smaller subproblems, each one involving one
input source, (ii) simultaneously optimizing the subproblems subject to certain relaxation of coupling
constraints, and (iii) combining the solutions of the subproblems in a certain way to obtain an
(approximately) optimal solution for the original problem.
We use our proposed framework to construct optimal or approximately optimal mechanisms for several settings
previously considered in the literature and to improve upon the best previously known results. We also
present applications of our techniques to non-mechanism design problems such as online stochastic generalized
assignment problem which itself captures online and stochastic versions of various other problems such as
resource allocation and job scheduling
