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Matrix Cubes Parametrized by Eigenvalues

2008/04/28 by Jiawang Nie, Bernd Sturmfels, Nie, Jiawang +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Robotic Mechanisms and Dynamics #math.AG #math.OC

paper · pdf · doi:10.48550/arxiv.0804.4462

12 pages, 1 figure

arxiv created 2008/04/28 · openalex publication_date 2008/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric matrices. An LMI representation is given for the convex set of all feasible instances, and its boundary is studied from the perspective of algebraic geometry. This generalizes the earlier work [12] with Parrilo on k-ellipses and k-ellipsoids.

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