A new primal-dual path-following interior-point algorithm for semidefinite optimization

Journal of Mathematical Analysis and Applications

Volumn 353, Issue 1, 2009, Pages 339-349

  Wang, G Q ^a,b   Bai, Y Q ^b  

^a SHANGHAI UNIVERSITY OF ENGINEERING SCIENCE   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Interior point algorithm; Iteration bound; Semidefinite optimization; Small update method

Indexed keywords

EID: 58149262934     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.12.016     Document Type: Article

References (22)

1. Achache M. A new primal-dual path-following method for convex quadratic programming. Appl. Comput. Math. 25 1 (2006) 97-110
2. Alizadeh F. Interior-point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim. 5 (1995) 13-51
3. Alizadeh F., Heaberly J.P.A., and Overton M.L. Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results. SIAM J. Optim. 8 3 (1998) 746-768
4. Bai Y.Q., El Ghami M., and Roos C. A new efficient large-update primal-dual interior-point method based on a finite barrier. SIAM J. Optim. 13 3 (2003) 766-782
5. Bai Y.Q., Lesaja G., Roos C., Wang G.Q., and El Ghami M. A class of large-update and small-update primal-dual interior-point algorithms for linear optimization. J. Optim. Theory Appl. 138 3 (2008) 341-359
6. Bai Y.Q., Roos C., and El Ghami M. A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM J. Optim. 15 1 (2004) 101-128
7. Bai Y.Q., and Wang G.Q. A new primal-dual interior-point algorithm for second-order cone optimization based on kernel function. Acta Math. Sin. (Engl. Ser.) 23 11 (2007) 2027-2042
8. Darvay Z. New interior-point algorithms in linear optimization. Adv. Model. Optim. 5 1 (2003) 51-92
9. Horn R.A., and Charles R.J. Topics in Matrix Analysis (1991), Cambridge University Press, UK
10. de Klerk E. Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications (2002), Kluwer Academic Publishers, Dordrecht, The Netherlands
11. Li X.S., He S.Y., Pan S.Y., and Zhang H.W. A path-following algorithm for linear complementarity problems based on algebraically equivalent transformation. J. Dalian Univ. Technol. 44 3 (2004) 337-341
12. Luo Z.Q., Sturm J., and Zhang S.Z. Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming. SIAM J. Optim. 8 (1998) 59-81
13. Nesterov Y.E., and Todd M.J. Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22 1 (1997) 1-42
14. Nesterov Y.E., and Todd M.J. Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. 8 2 (1998) 324-364
15. Pan S.Y., Li X.S., and He S.Y. An infeasible primal-dual interior-point algorithm for linear programs based on logarithmic equivalent transformation. J. Math. Anal. Appl. 314 (2006) 644-660
16. Peng J., Roos C., and Terlaky T. Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program. 93 (2002) 129-171
17. Todd M.J. A study of search directions in primal-dual interior-point methods for semidefinite programming. Optim. Methods Softw. 11 (1999) 1-46
18. Todd M.J., Toh K.C., and Tütüncü R.H. On the Nesterov-Todd direction in semidefinite programming. SIAM J. Optim. 8 3 (1998) 769-796
19. Vandenberghe L., and Boyd S. Semidefinite programming. SIAM Rev. 38 (1996) 49-95
20. Wang G.Q., Bai Y.Q., and Roos C. Primal-dual interior-point algorithms for semidefinite optimization based on a simple kernel function. J. Math. Model. Algorithms 4 (2005) 409-433
21. Wolkowicz H., Saigal R., and Vandenberghe L. Handbook of Semidefinite Programming, Theory, Algorithms, and Applications (2000), Kluwer Academic Publishers, Dordrecht, The Netherlands
22. Zhang Y. On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM J. Optim. 8 (1998) 365-386