Applications of Mathematics, Vol. 68, No. 4, pp. 441-465, 2023
The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem
Lu Zou, Yuan Lei
Received January 28, 2022. Published online February 3, 2023.
Abstract: For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the Generalized Eigenvalue Complementarity Problem (GEiCP) derived from unilateral friction elastic systems. Numerical experiments show the efficiency of the proposed methods compared to the projected steepest descent method with less CPU time.
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Affiliations: Lu Zou, Yuan Lei (corresponding author), School of Mathematics, Hunan University, Lushan Road (S), Yuelu District, Changsha 410082, P. R. China, e-mail: zoulu7@hnu.edu.cn, yleimath@hnu.edu.cn
