Bilinear Matrix Eigenvalue Optimization using Parallel Branch and Bound Method with Adaptive Computational Granularity

M. Kawanishi, T. Narikiyo, and T. Hashimoto (Japan)


bilinear matrix inequality, parallel branch and boundmethod, computational granularity


This paper shows a method for solving BMI (Bilinear Matrix Inequality) based on parallel branch and bound method. The computational granularity of parallelization is one of the key point for an efficient parallel algorithm. We here propose a parallel branch and bound algorithm that can automatically adjust the computational granularity to various BMI problems. In order to realize the automatic adaptation, we introduce an index measuring the complexity of BMI problems. Then, based on the index, we construct a model and estimate the optimal computational granularity. Numerical experiments are conducted to confirm the effectiveness of the proposed method.

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