| This monograph has grown from my PhD thesis Interior point Methods for Semidefinite Programming [39] which was published in December 1997. Since that time, Semidefinite Programming (SDP) has remained a popular research topic and the associated body of literature has grown considerably. As SDP has proved such a useful tool in many applications, like systems and control theory and combinatorial optimization, there is a growing number of people who would like to learn more about this field.
My goal with this monograph is to provide a personal view on the theory and applications of SDP in such a way that the reader will be equipped to read the relevant research literature and explore new avenues of research. Thus I treat a selected number of topics in depth, and provide references for further reading. The chapters are structured in such a way that the monograph can be used for a graduate course on SDP.
With regard to algorithms, I have focused mainly on methods involving the socalled Nesterov–Todd (NT) direction in some way. As for applications, I have selected interesting ones — mainly in combinatorial optimization — that are not extensively covered in the existing review literature.
In making these choices I hasten to acknowledge that much of the algorithmic analysis can be done in a more general setting (i.e., working with self-concordant barriers, self-dual cones and Euclidean Jordan algebras). I only consider real symmetric positive semidefinite matrix variables in this book; this already allows a wealth of applications. |
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