Of particular interest will be also the development of computational benchmarks and the integration of numerical optimization software with symbolic algebra packages. The problems and algorithms to be discussed arise from fields as diverse as functional analysis, control theory, probability theory, statistics, numerical algebraic geometry, combinatorics, multilinear algebra, and their applications in engineering and the life sciences. This workshop will focus on research directions at the interface of convex optimization and algebraic geometry, with both domains understood in the broadest sense. In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces in quantum cohomology. The latter includes approaches to polynomial optimization that are based on sums of squares, and new approximation hierarchies for hard combinatorial optimization problems. Particularly noteworthy is the cross-fertilization between Groebner bases and integer programming, and real algebraic geometry and semidefinite programming. In recent years new algorithms have been developed and this has lead to unexpected and exciting interactions with optimization theory. Algebraic geometry has a long and distinguished presence in the history of mathematics that produced both powerful and elegant theorems. Convex algebraic geometry involves the study of convex objects defined by real polynomial inequalities using the interplay of their convex and algebraic structure, with a special emphasis on those appearing in convex optimization.
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