Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function

Alizadeh, F., Haeberly, J. A. and Overton, M.: A new primal-dual interior-point method for semidefinite programming, in J. G. Lewis (ed.), Proceedings of the fifth SIAM Conference on Applied Linear Algebra, SIAM, 1994, pp. 113–117.

Andersen, E. D., Gondzio, J., Mészáros, Cs. and Xu, X.: Implementation of interior point methods for large scale linear programming, in T. Terlaky (ed.), Interior Point Methods of Mathematical Programming, Kluwer Academic Publishers, The Netherlands, 1996, pp. 189–252.

Bai, Y. Q. and Roos, C.: A primal-dual interior-point method based on a new kernel function with linear growth rate, in Proceedings of Industrial Optimization Symposium and Optimization Day, Australia, November 2002.

Bai, Y. Q., Ghami, M. El. and Roos, C.: A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization, SIAM J. Optim. 18 (2004), 101–128.

Ben-Tal, A. and Nemirovski, A.: Lectures on Modern Convex Optimization: Analysis, Algorithm, and Engineering Applications, MPS-SIAM Series on Optimization, Vol. 02, SIAM, Philadelphia, PA, 2001.

Helmberg, C., Rendl, F., Vanderbei, R. J. and Wolkowicz, H.: An interior-point method for semidefinite programming, SIAM J. Optim. 6 (1996), 342–361.

Horn, R. A. and Johnson, C. R.: Topics in Matrix Analysis, Cambridge University Press, 1991.

Kojima, M., Mizuno, S. and Yoshise, A.: Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM J. Optim. 7 (1997), 342–361.

Lütkepohl, H.: Handbook of Matrices, Wiley, 1996.

Megiddo, N.: Pathways to the optimal set in linear programming, in N. Megiddo (ed.), Progress in Mathematical Programming: Interior Point and Related Methods, Springer-Verlag, New York, 1989, pp. 131–158. Identical version in: Proceedings of the 6th Mathematical Programming Symposium of Japan, Nagoya, Japan, 1986, pp. 1–35.

Monteiro, R. D. C.: Primal-dual path-following algorithms for semidefinite programming, SIAM J. Optim. 7 (1997), 663–678.

Nesterov, Yu. E. and Todd, M. J.: Self-scaled barries and interior-point methods for convex programming, Math. Oper. Res. 22(1) (1997), 1–42.

Nesterov, Yu. E. and Todd, M. J.: Primal-dual interior-point methods for self-scaled cones, SIAM J. Optim. 8(2) (1998), 324–364 (electronic).

Peng, P., Roos, C. and Terlaky, T.: Self-regular functions and new search directions for linear and semidefinite optimization, Math. Programming 93 (2002), 129–171.

Peng, J., Roos, C. and Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms, Princeton University Press, 2002.

Roos, C., Terlaky, T. and Vial, J.-Ph.: Theory and Algorithms for Linear Optimization. An Interior-Point Approach, Wiley, Chichester, UK, 1997.

Sonnevend, G.: An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming, in A. Prékopa, J. Szelezsán and B. Strazicky (eds), System Modelling and Optimization: Proceedings of the 12th IFIP-Conference held in Budapest, Hungary, September 1985, Lecture Notes in Control and Inform. Sci. 84, Springer-Verlag, Berlin, 1986, pp. 866–876.

Wolkowicz, H., Saigal, R. and Vandenberghe, L.: Handbook of Semidefinite Programming, Theory, Algorithms, and Applications, Kluwer Academic Publishers, 2000.