Bounds for the BMI Eigenvalue Problem
Hisaya Fujioka, Kohta Hoshijima · Transactions of the Society of Instrument and Control Engineers · 1997
The Bilinear Matrix Inequality (BMI) eigenvalue problem is considered. Upper and Lower bounds of the BMI eigenvalue to combine with the BMI branch and bound algorithm are derived. The proposed lower bound is better in compare to existing one, and still computable via the LMI-optimization. While, the proposed upper bound is computationally cheap utilizing the lower bound optimizer. The worst case gap of the proposed bounds is characterized by the problem data. Numerical examples are also shown.