Jordan-algebraic approach to convexity theorem for quadratic mappings

Leonid Faybusovich (leonid.faybusovich.1nd.edu)

Abstract: We describe a Jordan-algebraic version of results related to convexity of images of quadratic mappings as well as related results on exactness of symmetric relaxations of certain classes of nonconvex optimization problems. The exactness of relaxations is proved based on rank estimates. Our approach provides a unifying viewpoint on a large number of classical results related to cones of Hermitian matrices over real and complex numbers. We describe (apparently new) results related to cones of Hermitian matrices with quaternion entries and the exceptional 27-dimensional Jordan algebra

Keywords: convexity, quadratic mappings, Jordan algebras

Category 1: Linear, Cone and Semidefinite Programming

Citation: to appear in SIOPT

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Entry Submitted: 06/24/2005
Entry Accepted: 06/25/2005
Entry Last Modified: 02/26/2006

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