Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

POLYNOMIAL CONVERGENCE OF PRIMAL-DUAL ALGORITHMS FOR SDLCP BASED ON THE M-Z FAMILY OF DIRECTIONS

  • Chen, Feixiang (School of Mathematics and Stistics, Chongqing Three-Gorges University)
  • Received : 2011.03.08
  • Accepted : 2011.06.16
  • Published : 2012.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

We establish the polynomial convergence of a new class of path-following methods for SDLCP whose search directions belong to the class of directions introduced by Monteiro [3]. We show that the polynomial iteration-complexity bounds of the well known algorithms for linear programming, namely the short-step path-following algorithm of Kojima et al. and Monteiro and Alder, carry over to the context of SDLCP.

Keywords

References

  1. Y. E. Nesterod and A. S. Nemirovskii, Interior Point methods in Convex Programming: Theory and Applications, SIAM, Philadelphia, 1994.
  2. Kojima.M, Shida.M, Shindoh.S, Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs. Mathematical Programming. 1998, 129-160.
  3. R. D. C. Monteiro, Primal-Dual Path-Following Algorithms for Semidefinite Programming, SIAM Journal on Optimization, Vol.7(1997), No.3, 663 - 678, 1997. https://doi.org/10.1137/S1052623495293056
  4. R. D. C. Monteiro, Polynomial convergence of primal-dual algorithms for semidefinite programming based on the Monteiro and Zhang family of directions , SIAM Journal on Optimization, Vol.8(1998), 797-812. https://doi.org/10.1137/S1052623496308618
  5. R. D. C. Monteiro and Y. Zhang, A unified analysis for a class of path-following primaldual interior-point algorithms for semidefinite programming, Math.program, 1998, 281-299.
  6. R. D. C. Monteiro and Y. Zhang, Polynomial convergence of a new family of primaldual algorithms for semidefinite programming, SIAM Journal on Optimization, Vol.9(1999), No.3, 551-577. https://doi.org/10.1137/S1052623496312836
  7. Yin Zhang, On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM Journal on Optimization. Vol.8(1998), No.2, 365-386. https://doi.org/10.1137/S1052623495296115
  8. M Shida, S Shindoh, M Kojima , Existence of search directions in interior-point algorithms for the SDP and the monotone SDLCP. SIAM Journal on Optimization, Vol.8(1998), No.2, 387-396. https://doi.org/10.1137/S1052623496300611