Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 2, page 5-19
  • ISSN: 0231-9721

Abstract

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Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is recommended as a suitable nonlinear rescaling function.

How to cite

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Andrášik, Richard. "Nonlinear Rescaling Method and Self-concordant Functions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.2 (2013): 5-19. <http://eudml.org/doc/260802>.

@article{Andrášik2013,
abstract = {Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is recommended as a suitable nonlinear rescaling function.},
author = {Andrášik, Richard},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {convex optimization; nonlinear rescaling method; self-concordant functions; convex optimization; nonlinear rescaling method; self-concordant functions},
language = {eng},
number = {2},
pages = {5-19},
publisher = {Palacký University Olomouc},
title = {Nonlinear Rescaling Method and Self-concordant Functions},
url = {http://eudml.org/doc/260802},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Andrášik, Richard
TI - Nonlinear Rescaling Method and Self-concordant Functions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 2
SP - 5
EP - 19
AB - Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is recommended as a suitable nonlinear rescaling function.
LA - eng
KW - convex optimization; nonlinear rescaling method; self-concordant functions; convex optimization; nonlinear rescaling method; self-concordant functions
UR - http://eudml.org/doc/260802
ER -

References

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  1. Boyd, S., Vandenberghe, L., Convex Optimization, Cambridge University Press, Cambridge, 2004. (2004) Zbl1058.90049MR2061575
  2. Griva, I., Nash, S. G., Sofer, A., Linear and Nonlinear Optimization, Second edition, SIAM, Philadelphia, 2009. (2009) Zbl1159.90002MR2472514
  3. Kučera, R., Machalová, J., Netuka, H., Ženčák, P., An interior-point algorithm for the minimization arising from 3D contact problems with friction, Optimization Methods and Software, (2013), in press. (2013) Zbl1278.65090MR3175463
  4. Nocedal, J., Wright, S. J., Numerical Optimization, Second edition, Springer, New York, 2006. (2006) Zbl1104.65059MR2244940
  5. Polyak, R., 10.1007/BF01586050, Mathematical Programming 54 (1992), 177–222. (1992) Zbl0756.90085MR1158819DOI10.1007/BF01586050
  6. Polyak, R., 10.1023/A:1010938423538, Annals of Operations Research 101 (2001), 427–460. (2001) Zbl0996.90088MR1852524DOI10.1023/A:1010938423538
  7. Polyak, R., Nonlinear rescaling vs. Smoothing Technique in Convex Optimization, Mathematical Programming 92A (2002), 197–235. (2002) Zbl1022.90014MR1901258
  8. Polyak, R., 10.1007/s10589-006-9759-0, Computational Optimization and Applications 35 (2006), 347–373. (2006) Zbl1128.90047MR2279496DOI10.1007/s10589-006-9759-0
  9. Polyak, R., Griva I., 10.1023/B:JOTA.0000041733.24606.99, JOTA 122, 1 (2004), 111–156. (2004) Zbl1129.90339MR2092474DOI10.1023/B:JOTA.0000041733.24606.99
  10. Polyak, R., Griva, I., Primal-Dual Nonlinear Rescaling Method with Dynamic Scaling Parameter Update, Mathematical Programming 106A (2006), 237–259. (2006) Zbl1134.90494MR2208083
  11. Polyak, R., Griva, I., 10.1007/s10898-006-9117-x, Journal of Global Optimization 40, 4 (2008), 679–695. (2008) Zbl1149.90146MR2377487DOI10.1007/s10898-006-9117-x
  12. Polyak, R., Griva, I., 10.3934/naco.2011.1.283, Numerical Algebra, Control and Optimization 1, 2 (2011), 283–299. (2011) Zbl1268.90046MR2805932DOI10.3934/naco.2011.1.283
  13. Polyak, R., Teboulle, M., 10.1007/BF02614440, Mathematical programming 76 (1997), 265–284. (1997) Zbl0882.90106MR1427187DOI10.1007/BF02614440

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