Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

  title={Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results},
  author={Farid Alizadeh and Jean-Pierre A. Haeberly and Michael L. Overton},
  journal={SIAM Journal on Optimization},
Primal-dual interior-point path-following methods for semidefinite programming are considered. Several variants are discussed, based on Newton’s method applied to three equations: primal feasibility, dual feasibility, and some form of centering condition. The focus is on three such algorithms, called the XZ, XZ+ZX, and Q methods. For the XZ+ZX and Q algorithms, the Newton system is well defined and its Jacobian is nonsingular at the solution, under nondegeneracy assumptions. The associated… CONTINUE READING
Highly Influential
This paper has highly influenced 34 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
218 Extracted Citations
9 Extracted References
Similar Papers

Citing Papers

Publications influenced by this paper.
Showing 1-10 of 218 extracted citations

Referenced Papers

Publications referenced by this paper.
Showing 1-9 of 9 references

On the NesterovTodd direction in semide nite programming

  • S. Boyd
  • 1996

On the superlinear andquadratic convergence of primaldual interior point linear programmingalgorithms

  • Y. Zhang, R. A. Tapia, J. E. Dennis
  • Technical ReportTR
  • 1995

Primal - dual potential reduction methodfor problems involving matrix inequalities

  • S. J. Wright.
  • Mathematical Programming ( Series B )
  • 1995

A new primaldualinteriorpoint method for semide nite programming

  • J. G. Lewis
  • 1994

Complementarityand nondegeneracy in semide nite programming

  • J. - P. A. Haeberly
  • Mathematical Programming Geometric Algorithms…
  • 1994

An interior - point method for semide nite programming

  • R. Vanderbei, H. Wolkowicz
  • SIAM Journal on Optimization
  • 1988

Similar Papers

Loading similar papers…