References
- Bai , Y. , El Ghami , M. and Roos , C. 2002 . A new efficient large-update primal–dual interior-point method based on a finite barrier . SIAM J. Optim , 13 : 766 – 782 .
- Bai , Y. , Roos , C. and Ghami , M. 2002 . A primal–dual interior-point method for linear optimization based on a new proximity function . Optim. Methods Softw , 17 : 985 – 1008 .
- Bai , Y. , El Ghami , M. and Roos , C. 2004 . A comparative study of kernel functions for primal–dual interior-point algorithms in linear optimization . SIAM J. Optim , 15 : 101 – 128 .
- El Ghami , M. “ New primal–dual interior-point methods based on kernel functions ” . Ph.D. thesis, Delft University of Technology, 2005
- Gu , G. “ Full-step interior-point methods for symmetric optimization ” . Ph.D. thesis, Delft University of Technology, 2009
- Gu , G. , Mansouri , H. , Zangiabadi , M. , Bai , Y. and Roos , C. 2010 . Improved full-Newton step O(nL) infeasible interior-point method for linear optimization . J. Optim. Theory Appl , 145 : 271 – 288 .
- Karmarkar , N. A new polynomial-time algorithm for linear programming . Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing . New York, NY, USA. pp. 302 – 311 .
- Kojima , M. , Megiddo , N. and Mizuno , S. 1993 . A primal–dual infeasible interior-point algorithm for linear programming . Math. Program , 61 : 263 – 280 .
- Lustig , I. 1990 . Feasibility issues in a primal–dual interior-point method for linear programming . Math. Program , 49 : 145 – 162 .
- Mansouri , H. “ Full-Newton step interior-point methods for conic optimization ” . Ph.D. thesis, Delft University of Technology, 2008
- Mansouri , H. and Roos , C. 2009 . A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization . Numer. Algorithms , 52 : 225 – 255 .
- Mansouri , H. , Zangiabadi , M. , Bai , Y. and Roos , C. 2008 . An infeasible interior-point algorithm with full-Newton step for linear optimization . Available at http://www.optimization-online.org/DB_HTML/2008/07/2052.html
- Mizuno , S. 1994 . Polynomiality of infeasible interior-point algorithms for linear programming . Math. Program , 67 : 109 – 119 .
- Peng , J. , Roos , C. and Terlaky , T. 2000 . New complexity analysis of the primal–dual Newton method for linear optimization . Ann. Oper. Res , 99 : 23 – 39 .
- Peng , J. , Roos , C. and Terlaky , T. 2001 . A new and efficient large-update interior-point method for linear optimization . Vychisl. Tekhnol , 6 : 61 – 80 .
- Peng , J. , Roos , C. and Terlaky , T. 2002 . Self-regular functions and new search directions for linear and semidefinite optimization . Math. Program , 93 : 129 – 171 .
- Peng , J. , Roos , C. and Terlaky , T. 2002 . Self-regularity: A New Paradigm for Primal-Dual Interior-point Algorithms , Princeton, NJ : Princeton University Press .
- Peng , J. , Terlaky , T. and Zhao , Y. 2005 . A predictor–corrector algorithm for linear optimization based on a specific self-regular proximity function . SIAM J. Optim , 15 : 1105 – 1127 .
- Roos , C. 2006 . A full-Newton step O(n) infeasible interior-point algorithm for linear optimization . SIAM J. Optim , 16 : 1110 – 1136 .
- Roos , C. , Terlaky , T. and Vial , J. 1997 . Theory and Algorithms for Linear Optimization: An Interior Point Approach , Chichester, , UK : John Wiley & Son Ltd .
- Salahi , M. , Terlaky , T. and Zhang , G. 2006 . The complexity of self-regular proximity based infeasible IPMs . Comput. Optim. Appl , 33 : 157 – 185 .
- Tanabe , K. 1988 . Centered Newton method for mathematical programming . Syst. Model. Optim , 113 : 197 – 206 .
- Wright , S. 1997 . Primal-Dual Interior-Point Methods , Philadelphia : Society for Industrial Mathematics, SIAM .
- Wu , F. , Wu , S. and Ye , Y. 1999 . On quadratic convergence of the OnL-iteration homogeneous and self-dual linear programming algorithm . Ann. Oper. Res , 87 : 393 – 406 .
- Ye , Y. 1997 . Interior Point Algorithms: Theory and Analysis , New York : John Wiley and Sons .
- Ye , Y. , Todd , M. and Mizuno , S. 1994 . An OnL-iteration homogeneous and self-dual linear programming algorithm . Math. Oper. Res , 19 : 53 – 67 .
- Zhang , Y. 1994 . On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem . SIAM J. Optim , 4 : 208 – 227 .
- Zhongyi , L. , Sun , W. and Fangbao , T. 2009 . A full-Newton step infeasible interior-point algorithm for linear programming based on a kernel function . Appl. Math. Optim , 60 : 237 – 251 .