The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem

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...

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Bibliographic Details
Published in:Applications of mathematics (Prague) 2023-08, Vol.68 (4), p.441-465
Main Authors: Zou, Lu, Lei, Yuan
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Classical and Continuum Physics
Eigenvalues
Elastic systems
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Steepest descent method
Theoretical
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Summary: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.
ISSN:0862-7940
1572-9109
DOI:10.21136/AM.2023.0020-22