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

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

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

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topChristina 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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