Ping Wang
ABSTRACT
In this paper, according to utilizing a self-adaptive technique, we present a self-adaptive trust region method for effectively solving tensor eigenvalue complementarity problems of various structures. Our proposed method demonstrates global convergence under suitable conditions. The numerical examples conducted in this study highlight the superior efficiency of our approach in comparison to the inexact Levenberg-Marquardt method and modified spectral PRP conjugate gradient method for computing tensor eigenvalue complementarity problems.
- Qi, L. 2005. Eigenvalues of a real super symmetric tensor. J. Symb. Comput. 40, 1302C1324Google Scholar
Digital Library
- Qi, L. 2007. Eigenvalues and invariants of tensors. J. Math. Anal. Appl. 325, 1363-1377Google ScholarCross Ref
- Ferris M C, Pang J. 1997. Engineering and Economic Applications of Complementarity Problems. SIAM Review. 39(4): 669-713.Google ScholarDigital Library
- Wardrop J G. 1953. Some Theoretical Aspects of Road Trallic Research. OR, 4(4):72-73.Google Scholar
- C. Ling, H. He and L. Qi. 2016. On the cone eigenvalue complementarity problem for higher-order tensors, Comput. Optim. Appl. 63 143C168.Google ScholarDigital Library
- C. Ling, H. He and L. Qi. 2016. Higher-degree eigenvalue complementarity problems for tensors, Comput. Optim. Appl. 64, 149C176.Google ScholarDigital Library
- Y. Liu and Q. Yang. 2018. A New Eigenvalue Complementarity Problem for Tensor and Matrix, Nankai University.Google Scholar
- H. Li, S. Du, Y. Wang and M. Chen. 2020. An inexact Levenberg-Marquardt method for tensor eigenvalue complementarity problem. Pacific J. Optim., 16, 87C99.Google Scholar
- Z. Chen and L. Qi. 2016. A semismooth Newton method for tensor eigenvalue complementarity problem. Comput. Optim. Appl., 65, 109C126Google ScholarDigital Library
- S. Adly and H. Rammal. 2013. A new method for solving Pareto eigenvalue complementarity problems. Comput. Optim. Appl., 55, 703C731.Google ScholarDigital Library
- Li Y , Du S Q , Chen Y Y. 2017. Modified spectral PRP conjugate gradient method for solving tensor eigenvalue c omplementarity problems[J]. Journal of industrial and management optimization, (18-1).Google Scholar
- G. Yu, Y. Song, Y. Xu and Z. Yu. 2019. Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems, Numer. Algorithms, 80, 1181C1201.Google Scholar
- C. Ling, H. He and L. Qi. 2016. Higher-degree eigenvalue complementarity problems for tensors, Comput. Optim. Appl., 64, 149C176.Google ScholarDigital Library
- Y. Liu and Q. Yang. 2018. A New Eigenvalue Complementarity Problem for Tensor and Matrix, Nankai UniversityGoogle Scholar
- Lu, Y., Li, W., Cao, M., Yang, Y. 2014. A novel self-adaptive trust region algorithm for unconstrained optimization. J. Appl Math. 1, 1C8Google Scholar
- Nocedal, J., Wright, S.J. 1999. Numerical Optimization. Springer, New YorkGoogle Scholar
- Yang, Y. 1999. On the truncated conjugate gradient method. Report, ICM99003, ICMSEC, Chinese Academy of Sciences. Beijing, ChinaGoogle Scholar
- Mingyuan C , Qingdao H, Yueting Y. 2018. A self-adaptive trust region method for extreme B-eigenvalues of symmetric tensors. Numerical AlgorithmsGoogle Scholar
Recommendations
Nonmonotone Trust-Region Methods for Bound-Constrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems
We develop and analyze a class of trust-region methods for bound-constrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a ...
A Global Convergence Theory for Dennis, El-Alem, and Maciel's Class of Trust-Region Algorithms for Constrained Optimization without Assuming Regularity
This work presents a convergence theory for Dennis, El-Alem, and Maciel's class of trust-region-based algorithms for solving the smooth nonlinear programming problem with equality constraints. The results are proved under very mild conditions on the ...
An Efficient Trust Region Algorithm for Minimizing Nondifferentiable Composite Functions
This paper presents a trust region algorithm for solving the following problem. Minimize $\phi (x) = f(x) + h(c(x))$ over $x \in R^n $, where f and c are smooth functions and h is a polyhedral convex function. Problems of this form include various ...
Comments