Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We investigate two monotone ascent spectral projected gradient (SPG) methods for TEiCP. We also present a shifted scaling-and-projection algorithm (SPA), which is a great improvement of the original SPA method proposed by Ling et al. (Comput. Optim. Appl. 63, 143–168 2016). Numerical comparisons with some existing gradient methods in the literature are reported to illustrate the efficiency of the proposed methods.