Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지

A Method of Sensitivity Analysis for the Infeasible Interior Point Method When a Variable is Added

변수추가시의 비가능 내부점기법의 감도분석

  • Kim, Woo-Je (Department of Industrial and Systems Engineering, Daejin University) ;
  • Park, Chan-kyoo (Department of IT Audit & Supervision, National Computerization Agency) ;
  • Lim, Sungmook (Department of Industrial Engineering, Seoul National University) ;
  • Park, Soondal (Department of Industrial Engineering, Seoul National University) ;
  • Murty , Katta G. (Department of Industrial and Operations Engineering, University of Michigan)
  • Published : 2002.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents a method of sensitivity analysis for the infeasible interior point method when a new variable is introduced. For the sensitivity analysis in introducing a new variable, we present a method to find an optimal solution to the modified problem. If dual feasibility is satisfied, the optimal solution to the modified problem is the same as that of the original problem. If dual feasibility is not satisfied, we first check whether the optimal solution to the modified problem can be easily obtained by moving only dual solution to the original problem. If it is possible, the optimal solution to the modified problem is obtained by simple modification of the optimal solution to the original problem. Otherwise, a method to set an initial solution for the infeasible interior point method is presented to reduce the number of iterations required. The experimental results are presented to demonstrate that the proposed method works better.

Keywords

References

  1. Adler, I. and Monteiro, D.D.C. (1992), A geometric view of parametric linear programming, Algorithmica, 8, 161-176
  2. Andersen, E.D., Gondzio, J., Meszaros, C. and Xu, Xiaojie (1996), Implementation of interior point methods for large scale linear programming, Technical Report, Logilab, HEC Geneva, Section of Management Studies, University of Geneva.
  3. Kim, W-J., Park, C-K., and Park, S. (1999), An ${\varepsilon}$-sensitivity analysis in the primal-dual interior point method," European Journal of Operational Research, 116, 629-639
  4. Kojima, M., Megiddo, N. and Mizuno, S. (1993), A primal-dual infeasible-interior-point algorithm for linear programming, Mathematical Programming, 61, 261-280
  5. Mehrotra, S. (1992), On the implementation of a primal-dual interior point method, SlAM Journal on Optimization, 2, 575-601
  6. Mehrotra, S. and Ye, Y. (1993), Finding an interior point in the optimal face of linear programs, Mathematical Programming, 62, 497-515
  7. Park, S. (1992), Linear Programming 3rd Ed., Minyoungsal, Seoul, Korea
  8. Park, S., Kim, W-J., Seol, T., Park, C., Seong, M. and Lim, S. (2001), Advanced Linear Programming, Kyowoosa, Seoul, Korea
  9. Park, S., Kim, W-J., Seol, T., Seong, M. and Park, C (2000), LPABO: a program for interior point methods for linear programming, Asis-Pacific Journal of Operational Research, 17, 81-100
  10. Yang, B. H. and Park, S. (1994), Sensitivity analysis on the cost coefficients for the Karmarkar's algorithm in linear programming, Proceedings of APORS 94, Hukuoka, Japan
  11. Zhang, Y. (1994), On the convergence of a class of infeasible-interior-point methods for the horizontal linear complementarity problem, SIAM Journal on Optimization, 4, 208-227