Modified spectral PRP conjugate gradient method for solving tensor eigenvalue complementarity problems

Abstract

Tensor eigenvalue complementary problems, as a special class of complementary problems, are the generalization of matrix eigenvalue complementary problems in higher-order. In recent years, tensor eigenvalue complementarity problems have been studied extensively. The research fields of tensor eigenvalue complementarity problems mainly focus on analysis of the theory and algorithms. In this paper, we investigate the solution method for four kinds of tensor eigenvalue complementarity problems with different structures. By utilizing an equivalence relation to unconstrained optimization problems, we propose a modified spectral PRP conjugate gradient method to solve the tensor eigenvalue complementarity problems. Under mild conditions, the global convergence of the given method is also established. Finally, we give related numerical experiments and numerical results compared with inexact Levenberg-Marquardt method, numerical results show the efficiency of the proposed method and also verify our theoretical results.

A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems

“…A spectral conjugate gradient method was designed using the spectral parameter and the conjugate parameter for large-scale UO [31]. A modified spectral PRP conjugate gradient method was presented for solving tensor eigenvalue complementarity problems and the numerical results were compared with the inexact Levenberg-Marquardt method [32]. Note that Table 1 indicates the advantages and evaluation tools of the existing methods of other researchers that can be reconciled and add new concepts into our proposed work.…”