Abstract
AbstractIn this paper, we consider a modified Levenberg–Marquardt algorithm for Low Order Value Optimization problems(LOVO). In the algorithm, we obtain the search direction by a combination of LM steps and approximate LM steps, and solve the subproblems therein by QR decomposition or cholesky decomposition. We prove the global convergence of the algorithm theoretically and discuss the worst-case complexity of the algorithm. Numerical results show that the algorithm in this paper is superior in terms of number of iterations and computation time compared to both LM-LOVO and GN-LOVO algorithm.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Andreani, R., Martinez, J.M., Martinez, L., Yano, F.S.: Low order-value optimization and applications. J. Global Optim. 43(1), 1–22 (2009)
2. Andreani, R., Dunder, C., Martinez, J.M.: Nonlinear-programming reformulation of the order-value optimization problem. Math. Methods Oper. Res. 61(3), 365–384 (2005)
3. Hodge, V., Austin, J.: A survey of outlier detection methodologies. Artif. Intell. Rev. 22(2), 85–126 (2004)
4. Law, J.: Robust statistics-the approach based on influence functions. J. Royal Stat. Soc. Ser. D Statist. 35(5), 565–566 (2018)
5. Andreani, R., Martinez, J.M., Martinez, L., Yano, F.: Continuous optimization methods for structure alignments. Math. Program. 112(1), 93–124 (2008)