# Generic Primal-dual Interior Point Methods Based on a New Kernel Function

RAIRO - Operations Research (2008)

- Volume: 42, Issue: 2, page 199-213
- ISSN: 0399-0559

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topEL Ghami, M., and Roos, C.. "Generic Primal-dual Interior Point Methods Based on a New Kernel Function." RAIRO - Operations Research 42.2 (2008): 199-213. <http://eudml.org/doc/250421>.

@article{ELGhami2008,

abstract = {
In this paper we present a generic primal-dual
interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as
proximity measure in the analysis of the algorithm. The proposed
kernel function does not satisfy all the conditions proposed in [2].
We show that the corresponding large-update
algorithm improves the iteration complexity with a factor
$n^\{\frac16\}$ when compared with the method based on the use of the
classical logarithmic barrier function. For small-update interior
point methods the iteration bound is
$O(\sqrt\{n\}\log\frac\{n\}\{\epsilon\}),$ which is currently the
best-known bound for primal-dual IPMs.
},

author = {EL Ghami, M., Roos, C.},

journal = {RAIRO - Operations Research},

keywords = {Linear optimization; primal-dual interior-point algorithm; large and small-update method.; linear optimization; large and small-update method},

language = {eng},

month = {5},

number = {2},

pages = {199-213},

publisher = {EDP Sciences},

title = {Generic Primal-dual Interior Point Methods Based on a New Kernel Function},

url = {http://eudml.org/doc/250421},

volume = {42},

year = {2008},

}

TY - JOUR

AU - EL Ghami, M.

AU - Roos, C.

TI - Generic Primal-dual Interior Point Methods Based on a New Kernel Function

JO - RAIRO - Operations Research

DA - 2008/5//

PB - EDP Sciences

VL - 42

IS - 2

SP - 199

EP - 213

AB -
In this paper we present a generic primal-dual
interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as
proximity measure in the analysis of the algorithm. The proposed
kernel function does not satisfy all the conditions proposed in [2].
We show that the corresponding large-update
algorithm improves the iteration complexity with a factor
$n^{\frac16}$ when compared with the method based on the use of the
classical logarithmic barrier function. For small-update interior
point methods the iteration bound is
$O(\sqrt{n}\log\frac{n}{\epsilon}),$ which is currently the
best-known bound for primal-dual IPMs.

LA - eng

KW - Linear optimization; primal-dual interior-point algorithm; large and small-update method.; linear optimization; large and small-update method

UR - http://eudml.org/doc/250421

ER -

## References

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