DOI QR코드

DOI QR Code

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR LINEAR PROGRAMMING BASED ON A SELF-REGULAR PROXIMITY

  • Liu, Zhongyi (College of Science, Hohai University) ;
  • Chen, Yue (Jincheng College, Nanjing University of Aeronautics and Astronautics)
  • Received : 2010.04.14
  • Accepted : 2010.06.21
  • Published : 2011.01.30

Abstract

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).

Keywords

References

  1. Z. Liu and W. Sun. An infeasible interior-point algorithm with full-Newton step for linear optimization. Numerical Algorithms, 46(2):173-188, 2007. https://doi.org/10.1007/s11075-007-9135-x
  2. Z. Liu and W. Sun. A full-Newton step infeasible interior-point algorithm for linear programming based on a kernel function. Applied Mathematics and Optimization, 60(2):237-251, 2009. https://doi.org/10.1007/s00245-009-9069-x
  3. H. Mansouri and C. Roos. Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton step. Optimization Methods and Software, 22(3):519-530, 2007. https://doi.org/10.1080/10556780600816692
  4. S. Mizuno. Polynomiality of infeasible-interior-point algorithms for linear programming. Mathematical Programming, 67(1):109-119, 1994. https://doi.org/10.1007/BF01582216
  5. J. Peng, C. Roos, and T. Terlaky. Self-regular functions and new search directions for linear and semidefinite optimization. Mathematical Programming, 93(1):129-171, 2002. https://doi.org/10.1007/s101070200296
  6. J. Peng and T. Terlaky. A dynamic large-update primal-dual interior-point method for linear optimization. Optimization Methods and Software, 17(6):1077-1104, 2002. https://doi.org/10.1080/1055678021000039175
  7. C. Roos, T. Terlaky, and J.-Ph.Vial. Theory and Algorithms for Linear Optimization. An Interior Approach. John Wiley and Sons, Chichester, UK, 1997.
  8. C. Roos. A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM Journal on Optimization, 16(4):1110-1136, 2006. https://doi.org/10.1137/050623917
  9. M. Salahi, T. Terlaky, and G. Zhang. The complexity of self-regular proximity based infeasible IPMs. Computational Optimization and Applications, 33(2):157-185, 2006. https://doi.org/10.1007/s10589-005-3064-1
  10. Y. Ye, M.J. Todd, and S. Mizuno. An O($\sqrt{n}L$)-iteration homogeneous and self-dual linear programming algorithm. Mathematical of Operations Research, 19(1):53-67, 1994. https://doi.org/10.1287/moor.19.1.53