# Rescaled proximal methods for linearly constrained convex problems

Paulo J.S. Silva; Carlos Humes

RAIRO - Operations Research (2007)

- Volume: 41, Issue: 4, page 367-380
- ISSN: 0399-0559

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topSilva, Paulo J.S., and Humes, Carlos. "Rescaled proximal methods for linearly constrained convex problems." RAIRO - Operations Research 41.4 (2007): 367-380. <http://eudml.org/doc/250138>.

@article{Silva2007,

abstract = {
We present an inexact interior point proximal method to solve
linearly constrained convex problems. In fact, we derive a
primal-dual algorithm to solve the KKT conditions of the
optimization problem using a modified version of the rescaled
proximal method. We also present a pure primal method.
The proposed proximal method has as distinctive feature the
possibility of allowing inexact inner steps even for Linear
Programming. This is achieved by using an error criterion that
bounds the subgradient of the regularized function, instead of using
ϵ-subgradients of the original objective function.
Quadratic convergence for LP is also proved using a more stringent
error criterion.
},

author = {Silva, Paulo J.S., Humes, Carlos},

journal = {RAIRO - Operations Research},

keywords = {Interior proximal methods; Linearly constrained convex
problems; interior proximal methods; linearly constrained convex problems},

language = {eng},

month = {10},

number = {4},

pages = {367-380},

publisher = {EDP Sciences},

title = {Rescaled proximal methods for linearly constrained convex problems},

url = {http://eudml.org/doc/250138},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Silva, Paulo J.S.

AU - Humes, Carlos

TI - Rescaled proximal methods for linearly constrained convex problems

JO - RAIRO - Operations Research

DA - 2007/10//

PB - EDP Sciences

VL - 41

IS - 4

SP - 367

EP - 380

AB -
We present an inexact interior point proximal method to solve
linearly constrained convex problems. In fact, we derive a
primal-dual algorithm to solve the KKT conditions of the
optimization problem using a modified version of the rescaled
proximal method. We also present a pure primal method.
The proposed proximal method has as distinctive feature the
possibility of allowing inexact inner steps even for Linear
Programming. This is achieved by using an error criterion that
bounds the subgradient of the regularized function, instead of using
ϵ-subgradients of the original objective function.
Quadratic convergence for LP is also proved using a more stringent
error criterion.

LA - eng

KW - Interior proximal methods; Linearly constrained convex
problems; interior proximal methods; linearly constrained convex problems

UR - http://eudml.org/doc/250138

ER -

## References

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