On the local convergence of a derivative-free algorithm for least-squares minimization

Computational Optimization and Applications

Volumn 51, Issue 2, 2012, Pages 481-507

  Zhang, Hongchao ^a   Conn, Andrew R ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Asymptotic convergence; Derivative free optimization; Least squares; Levenberg Marquardt method; Local convergence; System of nonlinear equations; Trust region

Indexed keywords

ASYMPTOTIC CONVERGENCE; DERIVATIVE-FREE OPTIMIZATION; LEAST SQUARE; LEVENBERG-MARQUARDT METHOD; LOCAL CONVERGENCE; SYSTEM OF NONLINEAR EQUATIONS; TRUST REGION;

COMPUTATIONAL METHODS; OPTIMIZATION;

ALGORITHMS;

EID: 84862022483     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-010-9367-x     Document Type: Article

References (21)

1. Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods. MPS-SIAM Series on Optimization. SIAM, Philadelphia (2000)
2. Conn, A.R., Scheinberg, K., Vicente, L.N.: Global convergence of general derivative-free trust-region algorithms to first and second order critical points. SIAM J. Optim. 20, 387-415 (2009)
3. Conn, A.R., Scheinberg, K., Vicente, L.N.: Geometry of interpolation sets in derivative free optimization. Math. Program. 111, 141-172 (2008) (Pubitemid 46993958)
4. Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. MPS-SIAM Series on Optimization. SIAM, Philadelphia (2009)
5. Conn, A.R., Scheinberg, K., Vicente, L.N.: Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation. IMA J. Numer. Anal. 28, 721-748 (2008)
6. Dan, H., Yamashita, N., Fukushima, M.: Convergence properties of the inexact Levenberg-Marquardt method under local error bound. Optim. Methods Softw. 17, 605-626 (2002) (Pubitemid 35350765)
7. Fan, J.: Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition. Comput. Optim. Appl. 34, 47-62 (2006) (Pubitemid 43723963)
8. Fan, J., Yuan, Y.: On the quadratic convergence of the Levenberg-Marquardt method without nonsin-gularity assumption. Computing 74, 23-39 (2005) (Pubitemid 40238398)
9. Hager, W.W., Zhang, H.: Self-adaptive inexact proximal point methods. Comput. Optim. Appl. 39, 161-181 (2008) (Pubitemid 351214604)
10. Hager, W.W., Zhang, H.: Asymptotic convergence analysis of a new class of proximal point methods. SIAM J. Control Optim. 46, 1683-1704 (2007)
11. Hock, W., Schittkowski, K.: Test examples for nonlinear programming codes. Lect. Notes Econ. Math. Syst. 187 (1981)
12. Moré, J.J.: The Levenberg-Marquardt algorithm, implementation and theory. In: Watson, G.A. (ed.) Numerical Analysis. Lecture Notes in Mathematics, vol. 630. Springer, Berlin (1977)
13. Powell, M.J.D.: Developments of NEWUOA for unconstrained minimization without derivatives. IMA J. Numer. Anal. 28, 649-664 (2008)
14. Powell, M.J.D.: The NEWUOA software for unconstrained optimization without derivatives. DAMTP (2004)
15. Powell, M.J.D.: Least Frobenius norm updating of quadratic models that satisfy interpolation conditions. Math. Program., Ser. B 100, 183-215 (2004) (Pubitemid 40871709)
16. Powell, M.J.D.: On trust region methods for unconstrained minimization without derivatives. Math. Program. 97, 605-623 (2003) (Pubitemid 44769762)
17. Tseng, P.: Error bounds and superlinear convergence analysis of some Newton-type methods in optimization. In: Di Pillo, G., Giannessi, F. (eds.) Nonlinear Optimization and Related Topics, pp. 445-462. Kluwer Academic, Dordrecht (2000)
18. Yamashita, N., Fukushima, M.: The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem. SIAM J. Optim. 11, 364-379 (2000) (Pubitemid 33357977)
19. Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg-Marquardt method. Computing 15, 237-249 (2001)
20. Zhang, H., Conn, A.R., Scheinberg, K.: A derivative-free algorithm for least-squares minimization. SIAM J. Optim. (2010, accepted)
21. Zhang, H., Conn, A.R., Scheinberg, K.: A derivative-free algorithm for least-squares minimization with bound constraints (2010, in preparation)