×

A parametrized Newton method for nonsmooth equations with finitely many maximum functions. (English) Zbl 1212.65203

Summary: We propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence of this method is proved and numerical experiments are listed.

MSC:

65H10 Numerical computation of solutions to systems of equations
PDFBibTeX XMLCite
Full Text: DOI EuDML Link

References:

[1] X. Chen, L. Qi: A parameterized Newton method and a quasi-Newton method for nonsmooth equations. Comput. Optim. Appl. 3 (1994), 157–179. · Zbl 0821.65029 · doi:10.1007/BF01300972
[2] F.H. Clarke: Optimization and Nonsmooth Analysis. John Wiley & Sons, New York, 1983. · Zbl 0582.49001
[3] Y. Gao: Newton methods for solving two classes of nonsmooth equations. Appl. Math. 46 (2001), 215–229. · Zbl 1068.65063 · doi:10.1023/A:1013791923957
[4] R. Mifflin: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control. Optim. 15 (1997), 959–972. · Zbl 0376.90081 · doi:10.1137/0315061
[5] J. S. Pang, L. Qi: Nonsmooth equations: Motivation and algorithms. SIAM J. Optim. 3 (1993), 443–465. · Zbl 0784.90082 · doi:10.1137/0803021
[6] F.A. Potra, L. Qi, D. Sun: Secant methods for semismooth equations. Numer. Math. 80 (1998), 305–324. · Zbl 0914.65051 · doi:10.1007/s002110050369
[7] L. Qi, J. Sun: A nonsmooth version of Newton’s method. Math. Program. Ser. A 58 (1993), 353–367. · Zbl 0780.90090 · doi:10.1007/BF01581275
[8] L. Qi: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18 (1993), 227–244. · Zbl 0776.65037 · doi:10.1287/moor.18.1.227
[9] M. J. Śmietański: An approximate Newton method for non-smooth equations with finite max functions. Numer. Algorithms 41 (2006), 219–238. · Zbl 1141.65031 · doi:10.1007/s11075-005-9009-z
[10] M. J. Śmietański: On a new class parametrized Newton-like methods for semismooth equations. Appl. Math. Comput. 193 (2007), 430–437. · Zbl 1193.65074 · doi:10.1016/j.amc.2007.03.075
[11] D. Sun, J. Han: Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM J. Optim. 7 (1997), 463–480. · Zbl 0872.90087 · doi:10.1137/S1052623494274970
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.