Geodesic
The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem
Applications of Mathematics, Tome 68 (2023) no. 4, pp. 441-465.

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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.
DOI : 10.21136/AM.2023.0020-22
Classification : 65F10, 65F20, 65F22, 65K10
Keywords: Pareto eigenvalue complementarity problem; generalized eigenvalue complementarity problem; nonlinear complementarity function; descent algorithm 
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Zou, Lu; Lei, Yuan. The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem. Applications of Mathematics, Tome 68 (2023) no. 4, pp. 441-465. doi : 10.21136/AM.2023.0020-22. http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0020-22/

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