# Dualities in Convex Algebraic Geometry

@article{Rostalski2010DualitiesIC, title={Dualities in Convex Algebraic Geometry}, author={Philipp Rostalski and Bernd Sturmfels}, journal={arXiv: Optimization and Control}, year={2010} }

Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article compares three notions of duality that are relevant in these contexts: duality of convex bodies, duality of projective varieties, and the Karush-Kuhn-Tucker conditions derived from Lagrange duality. We show that the optimal value of a polynomial program is an…

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