A modified infeasible interior-point algorithm with full-Newton step for semidefinite optimization

References

• F. Alizadeh, Combinatorial optimization with interior-point methods and semi-definite matrices, Ph.D. Thesis, University of Minnesota, Minneapolis, 1991.
   Google Scholar
• F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim. 5 (1995), pp. 13–51. doi: 10.1137/0805002
   Web of Science ®Google Scholar
• F. Alizadeh, J.A. Haeberly and M. Overton, Primal-dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results, SIAM J. Optim. 8 (1998), pp. 746–768. doi: 10.1137/S1052623496304700
   Web of Science ®Google Scholar
• Y. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM J. Optim. 13 (2003), pp. 766–782. doi: 10.1137/S1052623401398132
   Web of Science ®Google Scholar
• S.E. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM studies in Applied Mathematics, SIAM, Philadelphia, 1994.
   Google Scholar
• E. De Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, Kluwer Academic Publishers, Dordrecht, 2002.
   Google Scholar
• G. Gu, H. Mansouri, M. Zangiabadi, Y. Bai and C. Roos, Improved full-Newton step O(nL) infeasible interior-point method for linear optimization, J. Optim. Theory Appl. 145 (2010), pp. 271–288. doi: 10.1007/s10957-009-9634-0
   Web of Science ®Google Scholar
• C. Helmberg, F. Rendl, R.J. Vanderbei and H. Wolkowicz, An interior-point method for semidefinite programming, SIAM J. Optim. 6 (1996), pp. 342–361. doi: 10.1137/0806020
   Web of Science ®Google Scholar
• B. Kheirfam, Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step, Numer. Algor. 61 (2012), pp. 659–680. doi: 10.1007/s11075-012-9557-y
   Web of Science ®Google Scholar
• B. Kheirfam and N. Mahdavi-Amiri, A new inteior-point algorithm based on modified Nesterov-Todd direction for symmetric cone linear complementarity problem, Optim. Lett. 8 (2014), pp. 1017–1029. doi: 10.1007/s11590-013-0618-5
   Web of Science ®Google Scholar
• M. Kojima, N. Megiddo and S. Mizuno, A primal-dual infeasible-interior-point algorithm for linear programming, Math. Program. 61 (1993), pp. 263–280. doi: 10.1007/BF01582151
   Web of Science ®Google Scholar
• M. Kojima, S. Shindoh and S. Hara, Interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM J. Optim. 7 (1997), pp. 86–125. doi: 10.1137/S1052623494269035
   Web of Science ®Google Scholar
• J.B. Lasserre, Globle optimization with polynomials and the problems of moments, SIAM J. Optim. 11 (2005), pp. 796–817. doi: 10.1137/S1052623400366802
   Google Scholar
• Z. Liu and W. Sun, A full-NT-step infeasible interior-point algorithm for SDP based on kernel functions, Appl. Math. Comput. 217 (2011), pp. 4990–4999.
   Web of Science ®Google Scholar
• I.J. Lustig, Feasibile issues in a primal-dual interior point method for linear programming, Math. Program. 49 (1990), pp. 145–162. doi: 10.1007/BF01588785
   Web of Science ®Google Scholar
• H. Mansouri and C. Roos, A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization, Numer. Algor. 52 (2009), pp. 225–255. doi: 10.1007/s11075-009-9270-7
   Web of Science ®Google Scholar
• H. Mansouri, M. Zangiabadi and M. Arzani, A modified infeasible-interior-point algorithm for linear optimization problems, J. Optim. Theory Appl. 166 (2015), pp. 605–618. doi: 10.1007/s10957-015-0719-7
   Web of Science ®Google Scholar
• R.D.C. Monteiro, Primal-dual path-following algorithms for semidefinite programming, SIAM J. Optim. 7 (1997), pp. 663–678. doi: 10.1137/S1052623495293056
   Web of Science ®Google Scholar
• R.D.C. Monteiro and Y. Zhang, A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming, Math. Program. 81 (1998), pp. 281–299.
   Web of Science ®Google Scholar
• Y.E. Nesterov and A.S. Nemirovsky, Interior Point Methods in Convex Programming: Theory and Applications, SIAM, Philadelphia, 1994.
   Google Scholar
• Y.E. Nesterov and M.J. Todd, Self-scaled barriers and interior-point mehods for convex programming, Math. Oper. Res. 22 (1997), pp. 1–42. doi: 10.1287/moor.22.1.1
   Web of Science ®Google Scholar
• Y.E. Nesterov and M.J. Todd, Primal-dual interior-point methods for self-scaled cones, SIAM J. Optim. 8 (1998), pp. 324–364. doi: 10.1137/S1052623495290209
   Web of Science ®Google Scholar
• P.A. Parrilo, Semidefinite optimization relaxations for semialgebraic problems, Math. Program. 96 (2003), pp. 293–320. doi: 10.1007/s10107-003-0387-5
   Web of Science ®Google Scholar
• J. Peng, C. Roos and T. Terlaky, A new and efficient large-update interior-point method for linear optimization, J. Comput. Tech. 6 (2001), pp. 61–80.
   Google Scholar
• J. Peng, C. Roos and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization, Math. Program. Ser. A 93 (2002), pp. 129–171. doi: 10.1007/s101070200296
   Web of Science ®Google Scholar
• C. Roos, A full-Newton step O(n) infeasible interior-point algorithm for linear optimization, SIAM J. Optim. 16 (2006), pp. 1110–1136. doi: 10.1137/050623917
   Web of Science ®Google Scholar
• C. Roos, An improved and simplified full-Newton step O(n) infeasible interior-point method for linear optimization, SIAM J. Optim. 25 (2015), pp. 102–114. doi: 10.1137/140975462
   Web of Science ®Google Scholar
• K. Tanabe, Centered Newton method for linear programming: interior and ‘exterior’ point method (in Janpanese), in K. Tone, ed., New Methods for Linear Programming, The Institute of Statistical Mathematics, Tokyo, 3 (1990), pp. 98–100.
   Google Scholar
• M.J. Todd, K.C. Toh and R.H. Tütüncü, On the Nesterov-Todd direction in semidefinite programming, SIAM J. Optim. 8 (1998), pp. 769–796. doi: 10.1137/S105262349630060X
   Web of Science ®Google Scholar
• G. Wang, Y. Bai, X. Gao and D. Wang, Improved complexity analysis of full Nesterov-Todd step interior-point methods for semidefinite optimization, J. Optim. Theory Appl. 165 (2015), pp. 242–262. doi: 10.1007/s10957-014-0619-2
   Web of Science ®Google Scholar
• G. Wang, Y. Bai and C. Roos, Primal-dual interior-point algorithm for semidefinite optimization based on a simple kernel function, J. Math. Model. Algor. 4 (2005), pp. 409–433. doi: 10.1007/s10852-005-3561-3
   Google Scholar
• G. Wang, L. Kong, J. Tao and G. Lesaja, Improved complexity analysis of full Nesterov-Todd step feasible interior-point method for symmetric optimization, J. Optim. Theory Appl. 166 (2015), pp. 588–604. doi: 10.1007/s10957-014-0696-2
   Web of Science ®Google Scholar
• W. Wang, H. Liu and H. Bi, Simplified full Nesterov-Todd step infeasible interior-point algorithm for semidefinite optimization based on a kernel function, J. Appl. Math. Comput., pp. 1–19.
   PubMed Web of Science ®Google Scholar
• L. Zhang and Y. Xu, A full-Newton step interior-point algorithm based on modified Newton direction, Oper. Res. Lett. 39 (2011), pp. 317–322.
   Web of Science ®Google Scholar