本征问题是max-plus代数中的重要研究内容，具有广泛的应用背景。Sub本征问题及super本征问题是本征问题的延伸与推广，其中super本征问题至今仍是开问题。本项目拟从三个方面展开对super本征问题的研究：（1）将super本征问题等价地转化为不等式组A⊗X≥X的求解，结合已有算法设计出时间复杂度更低的求解不等式组解空间的生成集和基的有效算法，并以双边线性方程组的求解为基础提出计算不等式组的新算法；（2）深入探讨super本征向量空间的结构及真super本征向量的性质，找到矩阵的所有真super本征向量，进而实现super本征向量空间的完备刻画；（3）讨论特殊矩阵的super本征问题，提出求解算法，分析并比较一般情形与特殊情形的算法复杂度。Super本征问题的解决不但能推动本征问题的深入研究，同时也能为max-plus代数上双边线性方程组及不等式组的求解奠定基础。

The eigenproblem is of key importance in max-plus algebra, and the problem has extensive application background. Subeigenproblem and supereigenproblem are the extension of eigenproblem, and the supereigenproblem is still an open problem today. This project studies the supereigenproblem from the following three aspects: (1) The problem of solving the system of inequalities A⊗X≥X, which is equivalent to supereigenproblem, is discussed, and an effective algorithm with lower time complexity is proposed based on the existing algorithms to find a set of generators and a basis for the solution space of the system, and a new algorithm is proposed based on solving two-sided linear system. (2) Discuss the structure of supereigenspace and the properties of supereigenvectors, and find all proper supereigenvectors, and then fully characterize the supereigenspace. (3) The supereigenproblem for some special matrices is discussed, and an algorithm is designed, and the algorithm complexity in general and special cases is analyzed and compared. The aim of solving supereigenproblem is to promote the further study on eigenproblem and provide a base for solving two-sided linear system.