论文信息 - A logarithm barrier method for semi-definite programming

A logarithm barrier method for semi-definite programming

This paper presents a logarithmic barrier method for solving a semi-definite linear program. The descent direction is the classical Newton direction. We propose alternative ways to determine the step-size along the direction which are more efficient than classical line-searches.

Jean-Pierre Crouzeix | Bachir Merikhi | J. Crouzeix | B. Merikhi

[1] Michael L. Overton,et al. Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results , 1998, SIAM J. Optim..

[2] D K Smith,et al. Numerical Optimization , 2001, J. Oper. Res. Soc..

[3] J. Frédéric Bonnans,et al. Numerical Optimization: Theoretical and Practical Aspects (Universitext) , 2006 .

[4] H. Wolkowicz,et al. Bounds for eigenvalues using traces , 1980 .

[5] Ming Gu,et al. Primal-Dual Interior-Point Methods for Semidefinite Programming in Finite Precision , 1999, SIAM J. Optim..

[6] Stephen P. Boyd,et al. Semidefinite Programming , 1996, SIAM Rev..

[7] Michael L. Overton,et al. Semidefinite programming , 1997, Math. Program..

[8] A. Seeger,et al. New Bounds for the Extreme Values of a Finite Sample of Real Numbers , 1996 .

[9] Jean Charles Gilbert,et al. Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[10] Farid Alizadeh,et al. Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization , 1995, SIAM J. Optim..

[11] R. Tyrrell Rockafellar,et al. Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[12] Shinji Hara,et al. Interior Point Methods for the Monotone Linear Complementarity Problem in Symmetric Matrices , 1995 .

[13] Djamel Benterki,et al. A numerical implementation of an interior point method for semidefinite programming , 2003 .