改进的谱投影梯度法解张量特征值互补问题

An Improved Spectral Projected Gradient Method for Tensor Eigenvalue Complementarity Problems

对于对称且严格协正的张量,其张量特征值互补问题的特征值计算可等价为求解对应优化问题的稳定点。提出一种改进的谱投影梯度算法用于求解张量特征值互补问题的Pareto-特征值,并分析该算法的全局收敛性。数值结果表明:高维张量的情形下,改进后的谱投影梯度算法比现有的谱投影梯度算法在迭代次数和计算时间方面有较明显的优势,对初始迭代点的依赖程度较低,有较好的稳定性。

This paper considers a class of tensor eigenvalue complementarity problems with strictly copositive and symmetric tensors,which can be equivalently characterized as finding a stationary point of a related optimization problem.To find a Pareto-eigenvalue of the problem under consideration,we propose an improved spectral projected gradient(ISPG)method,which also has the global convergence property.Numerical experiments show that the proposed ISPG performs better than the existing spectral projected gradient methods in terms of taking less iterations and computational time.Moreover,the new algorithm is stable in the sense that it has relatively weak sensitivity to starting points.