Communications in Information and Systems

Volume 2 (2002)

Number 3

Newton’s algorithm in Euclidean Jordan algebras, with applications to robotics

Pages: 283 – 298

DOI: http://dx.doi.org/10.4310/CIS.2002.v2.n3.a5

Authors

Uwe Helmke (Department of Mathematics, University of Würzburg, Germany)

Sandra Ricardo (Department of Mathematics, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal)

Shintaro Yoshizawa (Department of Mathematics, University of Würzburg, Germany)

Abstract

We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algebras. The problem is solved using a damped Newton algorithm. Quadratic convergence to the global minimum is shown using an explicit step-size selection. Moreover, we prove that the algorithm is a smooth discretization of a Newton flow with Lipschitz continuous derivative.

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