Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities

Christina Jager

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 1, page 51-69
  • ISSN: 1509-9407

Abstract

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In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20] are used. Finally, some numerical results for non-smooth convex optimization problems are given which compare the hybrid algorithm to the inexact proximal point method from Rockafellar [17].

How to cite

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Christina Jager. "Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 51-69. <http://eudml.org/doc/271192>.

@article{ChristinaJager2007,
abstract = {In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20] are used. Finally, some numerical results for non-smooth convex optimization problems are given which compare the hybrid algorithm to the inexact proximal point method from Rockafellar [17].},
author = {Christina Jager},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {variational inequality; proximal point algorithm; bundle method},
language = {eng},
number = {1},
pages = {51-69},
title = {Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities},
url = {http://eudml.org/doc/271192},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Christina Jager
TI - Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 1
SP - 51
EP - 69
AB - In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20] are used. Finally, some numerical results for non-smooth convex optimization problems are given which compare the hybrid algorithm to the inexact proximal point method from Rockafellar [17].
LA - eng
KW - variational inequality; proximal point algorithm; bundle method
UR - http://eudml.org/doc/271192
ER -

References

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