2015/05/11 by Zhongming Chen, Chen, Zhongming, Qingzhi Yang +3 · 2 citations
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Power System Optimization and Stability #Spectral Theory (math.SP) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1505.02494
openalex publication_date 2015/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems. The general properties of the (GEiCP-T) have been studied. We establish its relationship with the generalized tensor eigenvalue problem. It follows that if exist, the number of λ-solutions can be bounded. We also give some sufficient conditions for the existence of the solution. In particular, there exists a unique solution of the (EiCP-T) (i.e., J=[n]) for irreducible nonnegative tensors. For the symmetric case, we derive a sufficient and necessary condition for the solvability of the (GEiCP-T) by reformulating it as a nonlinear program. It has also been proved that deciding the solvability of the (EiCP-T) is NP-hard in general. Moreover, a shifted projected power method is proposed to solve the symmetric (GEiCP-T). The monotonic convergence is also established. The numerical experiments demonstrate convergence behavior of our method and show that the algorithm presented is promising.