# A numerical feasible interior point method for linear semidefinite programs

Djamel Benterki; Jean-Pierre Crouzeix; Bachir Merikhi

RAIRO - Operations Research (2007)

- Volume: 41, Issue: 1, page 49-59
- ISSN: 0399-0559

## Access Full Article

top## Abstract

top## How to cite

topBenterki, Djamel, Crouzeix, Jean-Pierre, and Merikhi, Bachir. "A numerical feasible interior point method for linear semidefinite programs." RAIRO - Operations Research 41.1 (2007): 49-59. <http://eudml.org/doc/250116>.

@article{Benterki2007,

abstract = {
This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.
},

author = {Benterki, Djamel, Crouzeix, Jean-Pierre, Merikhi, Bachir},

journal = {RAIRO - Operations Research},

keywords = {Linear programming; semidefinite programming; interior point methods.},

language = {eng},

month = {6},

number = {1},

pages = {49-59},

publisher = {EDP Sciences},

title = {A numerical feasible interior point method for linear semidefinite programs},

url = {http://eudml.org/doc/250116},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Benterki, Djamel

AU - Crouzeix, Jean-Pierre

AU - Merikhi, Bachir

TI - A numerical feasible interior point method for linear semidefinite programs

JO - RAIRO - Operations Research

DA - 2007/6//

PB - EDP Sciences

VL - 41

IS - 1

SP - 49

EP - 59

AB -
This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.

LA - eng

KW - Linear programming; semidefinite programming; interior point methods.

UR - http://eudml.org/doc/250116

ER -

## References

top- F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim.5 (1995) 13–51.
- F. Alizadeh, J.P.A. Haeberly and M.L. Overton, Primal-dual interior point methods for semidefinite programming: convergence rates, stability and numerical results. SIAM J. Optim.8 (1998) 746–768.
- S.J. Benson, Y. Ye and X. Zhang, Solving large-scale sparse semidefinite programs for combinatorial optimization. SIAM J. Optim.10 (2000) 443–461.
- P. Gahinet, A. Nemirovski, The projective method for solving linear matrix inequalities. Math. Program.77 (1997) 163–190.
- C. Helmberg, F. Rendl, R.J. Vanderbei and H. Wolkowicz, An interior point method for semidefinite programming. SIAM J. Optim.6 (1996) 342–361.
- M. Kojima, S. Shindoh and S. Hara, Interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM J. Optim.7 (1997) 86–125.
- Y. Nesterov and A. Nemirovski, Interior point polynomial algorithms in convex programming. SIAM Stud. Appl. Math.13, Society for Industrial and applied Mathematics (SIAM), Philadelphia, PA (1994).
- A. Nemirovski and K. Scheinberg, Extension of Karmarkar's algorithm onto convex quadratically constrained quadratic problems. Math. Program.72 (1996) 273–289.
- M. Overton and H. Wolkowicz, Semidefinite programming. Math. Program.77 (1997) 105–109.
- M.V. Ramana, L. Tuncel and H. Wolkowicz, Strong duality for semidefinite programming. SIAM J. Optim.7 (1997) 641–662.
- L. Vandenberghe and S. Boyd, Positive definite programming. SIAM Rev.38 (1996) 49–95.
- H. Wolkowicz, G.-P.-H. Styan, Bounds for eigenvalues using traces. Linear Algebra Appl.29 (1980) 471–506.
- sdplib/ URIhttp://infohost.nmt.edu/

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.