this course we present a survey of topics on the subject of semidefinite
programming. We attempt to make the course both deep and comprehensive.
Each student should take turn and jot down lecture note in class. Then
within a week of the lecture the students should transcribe the notes into
Latex and e-mail the notes to me so I post it in the course home page.
Below I have a list of topics I wish to cover, but this is most likely
more than what we can reasonably cover in one semester. So we probably
cover a subset.
Topic 3: Introduction to Euclidean Jordan algebras and symmetric cones. How do LP, QCQP and SDP are related? How can one set of proofs and analysis be used for all of them?
Topic 4: Interior point methods for SDP, notion of logarithmic barrier, potential functions, central path and the notion of proximity to central path, algorithms with polynomial-time iteration complexity. Notion of feasibility and boundedness and how the situation is different from linear programming. Primal-dual methods, the XS, SX, Nesterov-Todd, and XS+SX methods, Moneiro-Zhang family of classes, the commutative class of algorithms, polynomial-time path-following methods.
Topic 5: Problems that can be formulated as SDP and related optimization models. Various Eigenvalue optimization problems, Nesterov-Nemirovskii's class of methods for formulating various problems in SDP format. Sum of norms minimization.
Topic 6: The Lovasz theta function and SDP, Goemans and Williamson's approximation algorithm for MAXCUT and related problems.
Topic 7: Applications in Statistics and Finance, optimal design of experiments and SDP, robust linear programming, Markowitz portfolio selection problems,.
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