- Homework.......................... 50%
- Final Take-home Exam.......... 50%
COURSE TOPICS OUTLINE - C&O 370
Though these problems have been studied before, it is only recently that the combination of important applications with implementable algorithms has resulted in intensive research activity. This area is proving to be of major importance because of the many applications; in addition, the high mathematical elegance is attracting many researchers.
This course will provide a thorough treatment of semidefinite programming.
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THEORY
- Convex analysis on symmetric matrices
- Geometry of SDP
- First and second order optimality conditions; duality
- Error analysis and parametric programming
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ALGORITHMS
- Potential reduction methods
- path-following methods
- implementation
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APPLICATIONS
- Combinatorial Optimization problems (e.g. quadratic assignment, graph partitioning, max-cut, general integer)
- eigenvalue optimization
- matrix completion problems
- nonconvex quadratic optimization
This course is supported partially by the Fields Institute
