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Tight bounds on Lyapunov rank

Michael Orlitzky (michael***at***orlitzky.com)

Abstract: The Lyapunov rank of a cone is the number of independent equations obtainable from an analogue of the complementary slackness condition in cone programming problems, and more equations are generally thought to be better. Bounding the Lyapunov rank of a proper cone in R^n from above is an open problem. Gowda and Tao gave an upper bound of n^2 - n that was later improved by Orlitzky and Gowda to (n-1)^2 . We settle the matter and show that the Lyapunov rank of (n^2 - n)/2 + 1 belonging to the Lorentz second-order cone is maximal.

Keywords: Lyapunov rank, bilinearity rank, Lorentz cone, second-order cone

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Complementarity and Variational Inequalities

Category 3: Global Optimization

Citation: July 21st, 2020

Download: [PDF]

Entry Submitted: 07/21/2020
Entry Accepted: 07/21/2020
Entry Last Modified: 08/12/2020

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