# Interior proximal method for variational inequalities on non-polyhedral sets

Alexander Kaplan; Rainer Tichatschke

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

- Volume: 27, Issue: 1, page 71-93
- ISSN: 1509-9407

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topAlexander Kaplan, and Rainer Tichatschke. "Interior proximal method for variational inequalities on non-polyhedral sets." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 71-93. <http://eudml.org/doc/271153>.

@article{AlexanderKaplan2007,

abstract = {Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of the method studied admits the use of the 𝝐-enlargement of the operator and an inexact solution of the subproblems.},

author = {Alexander Kaplan, Rainer Tichatschke},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {variational inequalities; Bregman function; proximal algorithm; Bergman function},

language = {eng},

number = {1},

pages = {71-93},

title = {Interior proximal method for variational inequalities on non-polyhedral sets},

url = {http://eudml.org/doc/271153},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Alexander Kaplan

AU - Rainer Tichatschke

TI - Interior proximal method for variational inequalities on non-polyhedral sets

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2007

VL - 27

IS - 1

SP - 71

EP - 93

AB - Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of the method studied admits the use of the 𝝐-enlargement of the operator and an inexact solution of the subproblems.

LA - eng

KW - variational inequalities; Bregman function; proximal algorithm; Bergman function

UR - http://eudml.org/doc/271153

ER -

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