A parametrized Newton method for nonsmooth equations with finitely many maximum functions

Shou-qiang Du; Yan Gao

Applications of Mathematics (2009)

  • Volume: 54, Issue: 5, page 381-390
  • ISSN: 0862-7940

Abstract

top
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.

How to cite

top

Du, Shou-qiang, and Gao, Yan. "A parametrized Newton method for nonsmooth equations with finitely many maximum functions." Applications of Mathematics 54.5 (2009): 381-390. <http://eudml.org/doc/37828>.

@article{Du2009,
abstract = {In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.},
author = {Du, Shou-qiang, Gao, Yan},
journal = {Applications of Mathematics},
keywords = {nonsmooth equations; Newton method; convergence; numerical examples; nonsmooth equations; Newton method; convergence; numerical examples},
language = {eng},
number = {5},
pages = {381-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A parametrized Newton method for nonsmooth equations with finitely many maximum functions},
url = {http://eudml.org/doc/37828},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Du, Shou-qiang
AU - Gao, Yan
TI - A parametrized Newton method for nonsmooth equations with finitely many maximum functions
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 5
SP - 381
EP - 390
AB - In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
LA - eng
KW - nonsmooth equations; Newton method; convergence; numerical examples; nonsmooth equations; Newton method; convergence; numerical examples
UR - http://eudml.org/doc/37828
ER -

References

top
  1. Chen, X., Qi, L., 10.1007/BF01300972, Comput. Optim. Appl. 3 (1994), 157-179. (1994) Zbl0821.65029MR1273659DOI10.1007/BF01300972
  2. Clarke, F. H., Optimization and Nonsmooth Analysis, John Wiley & Sons New York (1983). (1983) Zbl0582.49001MR0709590
  3. Gao, Y., 10.1023/A:1013791923957, Appl. Math. 46 (2001), 215-229. (2001) Zbl1068.65063MR1828306DOI10.1023/A:1013791923957
  4. Mifflin, R., 10.1137/0315061, SIAM J. Control. Optim. 15 (1997), 959-972. (1997) MR0461556DOI10.1137/0315061
  5. Pang, J. S., Qi, L., 10.1137/0803021, SIAM J. Optim. 3 (1993), 443-465. (1993) Zbl0784.90082MR1230150DOI10.1137/0803021
  6. Potra, F. A., Qi, L., Sun, D., 10.1007/s002110050369, Numer. Math. 80 (1998), 305-324. (1998) Zbl0914.65051MR1645041DOI10.1007/s002110050369
  7. Qi, L., Sun, J., 10.1007/BF01581275, Math. Program. Ser. A 58 (1993), 353-367. (1993) Zbl0780.90090MR1216791DOI10.1007/BF01581275
  8. Qi, L., 10.1287/moor.18.1.227, Math. Oper. Res. 18 (1993), 227-244. (1993) Zbl0776.65037MR1250115DOI10.1287/moor.18.1.227
  9. Śmietański, M. J., 10.1007/s11075-005-9009-z, Numer. Algorithms 41 (2006), 219-238. (2006) Zbl1141.65031MR2222248DOI10.1007/s11075-005-9009-z
  10. Śmietański, M. J., 10.1016/j.amc.2007.03.075, Appl. Math. Comput. 193 (2007), 430-437. (2007) MR2385800DOI10.1016/j.amc.2007.03.075
  11. Sun, D., Han, J., 10.1137/S1052623494274970, SIAM J. Optim. 7 (1997), 463-480. (1997) Zbl0872.90087MR1443629DOI10.1137/S1052623494274970

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.