A primal-dual potential reduction method for problems involving matrix inequalities

@article{Vandenberghe1995APP,
  title={A primal-dual potential reduction method for problems involving matrix inequalities},
  author={Lieven Vandenberghe and Stephen P. Boyd},
  journal={Math. Program.},
  year={1995},
  volume={69},
  pages={205-236}
}
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga and Todd's method for linear programming. A worst-case analysis shows that the number of iterations grows as the square root of the problem size, but in practice it appears to grow more slowly. As in other interior-point methods the overall computational effort is therefore dominated by the least… CONTINUE READING
Highly Cited
This paper has 398 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 127 extracted citations

A recurrent neural network for real-time semidefinite programming

IEEE Trans. Neural Networks • 1999
View 6 Excerpts
Highly Influenced

Linear Matrix Inequalities in System and Control Theory [Book Reviews]

IEEE Transactions on Automatic Control • 1997
View 2 Excerpts
Highly Influenced

A New Primal-dual Interior-point Method for Semideenite Programming

Farid Alizadehy, Jean-Pierre A. Haeberlyz, Michael L. Overtonx
1994
View 5 Excerpts
Highly Influenced

398 Citations

02040'93'98'04'10'16
Citations per Year
Semantic Scholar estimates that this publication has 398 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 36 references

Interior-point polynomial methods in convex programming, Volume 13 of Studies in Applied Mathematics (SIAM

Yu. Nesterov, A. Nemirovsky
1994
View 13 Excerpts
Highly Influenced

Interior point polynomial time method for truss topology design

A. Ben Tal, A. Nemirovskii
Technical Report 3/92, Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology • 1992
View 10 Excerpts
Highly Influenced

and T . Terlaky , " A large - step analytic center method for a class of smooth convex programming problems "

C. Roos Den Hertog
Linear Matrix lnequalities in System and Control Theo ~ , Studies in Applied Mathematics • 1994

An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices

F. Jarre
SIAM Journal on Control and Optimization 31 • 1993
View 1 Excerpt

Algorithms for minimum trace factor analysis

G. A. Watson
SIAM Journal on Matrix Analysis and Applications 13 • 1992
View 1 Excerpt

Computational experience with a primal-dual interior-point method for smooth convex programming

J.-P. Vial
Technical report, D epartement d'Economie Commerciale et Industrielle, Universit e de Gen eve • 1992
View 1 Excerpt

Implementation of a primal null-space a ne scaling method and its extensions

K. Kim, J. L. Nazareth
Technical report, Department of Pure and Applied Mathematics, Washington State University • 1992
View 2 Excerpts