Journal of applied mathematics & informatics

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

POLYNOMIAL COMPLEXITY OF PRIMAL-DUAL INTERIOR-POINT METHODS FOR CONVEX QUADRATIC PROGRAMMING

  • Liu, Zhongyi (College of Science, Hohai University) ;
  • Sun, Wenyu (School of Mathematics and Computer Science, Nanjing Normal University) ;
  • De Sampaio, Raimundo J.B. (Pontifical Catholic University of Parana (PUCPR), Graduate Program in Production and Systems Engineering (PPGEPS))
  • 발행 : 2009.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.

키워드

참고문헌

  1. M. Achache. A new primal-dual path-followingmethod for convex quadratic programming. Computational & Applied Mathematics, 25(1):97-110, 2006.
  2. Z. Liu and W. Sun. An infeasible interior-point algorithm with full-Newton step for linear optimization. Numerical Algorithm, 46(2):173–188, 2007. https://doi.org/10.1007/s11075-007-9135-x
  3. J. Peng, C. Roos, and T. Terlaky. A new and efficient large-update interior-point method for linear optimization. Journal of Computational Technologies, 6(4):61–80, 2001.
  4. J. Peng, C. Roos, and T. Terlaky. A new class of polynomial primal-dualmethods for linear and semidefinite optimization. European Journal of Operational Research, 143(2):234–256, 2002. https://doi.org/10.1016/S0377-2217(02)00275-8
  5. J. Peng, C. Roos, and T. Terlaky. Self-regular functions and new search directions for linear and semidefinite optimization. Mathematial Programming, 93(1):129–171, 2002. https://doi.org/10.1007/s101070200296
  6. J. Peng, C. Roos, and T. Terlaky. Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms, Princeton University Press, Princeton, New Jersey, 2002.
  7. C. Roos, T. Terlaky, and J.-Ph.Vial. Theory and Algorithms for Linear Optimization. An Interior Approach, John Wiley & Sons, Chichester, UK, 1997.
  8. W. Sun and Y. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, New York, 2006.