This thesis presents two applications of combinatorial optimization. The first part contains a detailed description of a conference scheduling problem. We model the problem as a symmetric clustering problem, or a variant of minimum k -partition we call capacitated k -partition .…
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The related tasks of certifying bounds on optimization problems and refuting unsatisfiable systems of constraints have a long history in computer science and optimization, and deep mathematical roots in the proof complexity of algebraic systems. From the algorithmic perspective,…
Real algebraic geometry has a long and beautiful history going back to the 1800s. It is the study of real polynomials using algebraic techniques. Convex optimization plays a key role in applied mathematics and engineering, studying the geometric structure of convex sets that ari…
<P>Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms,…
Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, co…
This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geomet…
This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geomet…