A New Infeasible Interior-Point Method Based on a Non-Coercive Kernel Function with Improved Centering Steps for Second-Order Cone Optimization

REFERENCES

• K. Ahmadi , F. Hasani , and B. Kheirfam ( 2014 ). A full-Newton step infeasible interior-point algorithm based on Darvay directions for linear optimization . J. Math. Model. Algorithms Oper. Res. 13 : 191 – 208 .
   Google Scholar
• F. Alizadeh and D. Goldfarb ( 2003 ). Second-order cone optimization . Math. Program. 95 : 3 – 51 .
   Web of Science ®Google Scholar
• Y. Bai , M. El Ghami , and C. Roos ( 2002 ). A new efficient large update primal-dual interior-point method based on a finite barrier . SIAM J. Optim. 13 : 766 – 782 .
   Web of Science ®Google Scholar
• S. Bouali and S. Kabbaj ( 2014 ). Full-NT step infeasible interior-point method for SOCO based on a specific kernel function . Afr. Mat. 25 : 549 – 565 .
   Google Scholar
• Z. Darvay ( 2003 ). New interior point algorithms in linear programming . Adv. Model. Optim. 5 : 51 – 92 .
   Google Scholar
• Z. Darvay , I. M. Papp , and P. R. Takács ( 2014 ). An infeasible full-Newton step algorithm for linear optimization with one centering step in major iteration . Studia Univ. Babes-Bolyai, Informatica. LIX ( 1 ): 28 – 45 .
   Google Scholar
• L. Faybusovich ( 1997 ). Linear systems in Jordan algebras and primal-dual interior point algorithms . J. Comput. Appl. Math. 86 : 149 – 175 .
   Web of Science ®Google Scholar
• G. Gu , M. Zangiabadi , and C. Roos ( 2011 ). Full Nesterov-Todd step infeasible interior-point method for symmetric optimization . European J. Oper. Res. 214 : 473 – 484 .
   Web of Science ®Google Scholar
• B. Kheirfam ( 2013 ). A new infeasible interior-point method based on Darvay's technique for symmetric optimization . Ann. Oper. Res. 211 : 209 – 224 .
   Web of Science ®Google Scholar
• B. Kheirfam and N. Mahdavi-Amiri (2014). A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem. Bull. Iranian Math. Soc. 40: 541–564.
   Google Scholar
• B. Kheirfam and F. Hasani (2014). A full-Newton step infeasible interior-point method for linear optimization based on an exponential kernel function. Asian-Eur. J. Math. 7:1450018 (14 pp.).
   Google Scholar
• M. S. Lobo , L. Vandenberghe , S. E. Boyd , and H. Lebret ( 1998 ). Applications of the second-order cone programming . Linear Algebra Appl. 284 : 193 – 228 .
   Web of Science ®Google Scholar
• Y. E. Nesterov and M. J. Todd ( 1997 ). Self-scaled barriers and interior-point methods for convex programming . Math. Oper. Res. 22 : 1 – 42 .
   Web of Science ®Google Scholar
• Y. E. Nesterov and M. J. Todd ( 1998 ). Primal-dual interior-point methods for self-scaled cones . SIAM J. Optim. 8 : 324 – 364 .
   Web of Science ®Google Scholar
• C. Roos , T. Terlaky , and J.-P. Vial (1997). Theory and Algorithms for Linear Optimization. An Interior-Point Approach . John Wiley and Sons , Chichester , UK.
   Google Scholar
• C. Roos ( 2006 ). A full-Newton step O(n) infeasible interior-point algorithm for linear optimization . SIAM J. Optim. 16 : 1110 – 1136 .
   Web of Science ®Google Scholar
• S. H. Schmieta and F. Alizadeh ( 2003 ). Extension of primal-dual interior-point algorithms to symmetric cones . Math. Program. 96 : 409 – 438 .
   Web of Science ®Google Scholar
• J. F. Sturm ( 2000 ). Similarity and other spectral relations for symmetric cones . Linear Algebra Appl. 312 : 135 – 154 .
   Web of Science ®Google Scholar
• G. Q. Wang and Y. Q. Bai ( 2012 ). A new full Nesterov-Todd step primal-dual path-following interior-point algorithm for symmetric optimization . J. Optim. Theory Appl. 154 : 966 – 985 .
   Web of Science ®Google Scholar
• G. Q. Wang and Y. Q. Bai ( 2009 ). A primal-dual interior-point algorithm for second-order cone optimization with full Nesterov-Todd step . Appl. Math. Comput. 215 : 1047 – 1061 .
   Web of Science ®Google Scholar
• M. Zangiabadi , G. Gu , and C. Roos ( 2013 ). A full Nesterov-Todd step infeasible interior-point method for second-order cone optimization . J. Optim. Theory Appl. 158 : 816 – 858 .
   Web of Science ®Google Scholar