CWI Amsterdam: EIDMA/DIAMANT minicourse by Pablo Parrilo

31-5-2010 - 4-6-2010

Lecturer: Pablo Parrilo.
In due time, see this page for details.

Title: Algebraic Optimization and Semidefinite Programming.
Abstract: This minicourse will focus on theoretical and computational techniques for
optimization problems with algebraic structure (in particular, those
involving polynomial equations and inequalities), emphasizing the
connections with techniques based on semidefinite programming (SDP).

The course will develop in a parallel fashion several algebraic and
numerical approaches to polynomial systems, with a view towards methods
that simultaneously incorporate both elements. We will study both the
complex and real cases, developing techniques of general applicability,
and stressing convexity-based ideas, complexity results, and efficient
implementations. We will use examples from several applied math and
engineering areas, including systems and control, geometric theorem
proving, and classical and quantum information theory.

Among the topics covered we will have: semidefinite relaxations, sum of
squares representations, hyperbolic polynomials, SDP representability of
convex sets, complex and real Nullstellensatz, convex algebraic geometry,
sparsity and rank minimization problems, etc.

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