An adaptive primal-dual full-Newton step infeasible interior-point algorithm for linear optimization
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. \cite{Arzani}. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter $\theta$. This value is adapted with the value of proximity function $\delta$ related to $(x\k y\k s)$ in current iteration of the algorithm. We derive a suitable interval to change the parameter $\theta$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that $\theta$ takes a default fixed value.
Abstract
In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. \cite{Arzani}. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter $\theta$. This value is adapted with the value of proximity function $\delta$ related to $(x\k y\k s)$ in current iteration of the algorithm. We derive a suitable interval to change the parameter $\theta$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that $\theta$ takes a default fixed value.
참고문헌 (15)
- Zs. Darvay, "An infeasible full-Newton step algorithm for linear optimization with one centering step in major iteration", Studia Univ. Babes Bolyai Inform, 59(1), pp.28~45 (2014)
- G. Gu, "Full Nesterov-Todd step infeasible interior-point methods for symmetric optimization", European J. Oper. Res, 214(3), pp.473~484 (2011)
- N. K. Karmarkar, "A new polynomial-time algorithm for linear programming", Combina-torica, 4(4), pp.373~395 (1984)
- H. Mansouri, "A simplified O(nL) infeasible interior-point algorithm for linear optimization using full Newton steps", Optim. Methods Softw, 22(3), pp.519~530 (2007)
- H. Mansouri, "An adaptive infeasible interior-point algorithm with full-Newton step for linear optimization", Optimization, 62(2), pp.285~297 (2013)
- H. Mansouri, "A modified infeasible-interior-point al-gorithm for linear optimization problems", J. Optim. Theory Appl, 166(2), pp.605~618 (2015)
- H. Mansouri, "A full-Newton step O(n) infeasible interior-point algorithm for linear complementarity problems", Nonlinear Anal. Real World Appl, 12(1), pp.545~561 (2011)
- C. Roos, "A full-Newton step O(n) infeasible interior-point algorithm for linear opti-mization", SIAM J. Optim, 16(4), pp.1110~1136 (2006)
- C. Roos, "An improved and simplified full-Newton step O(n) infeasible interior-point method for linear optimization", SIAM J. Optim, 25(1), pp.102~114 (2015)
- Gy. Sonnevend, "An Analytic Center for Polyhedrons and New Classes of Global Al-gorithms for Linear (Smooth, Convex) Programming", pp.866~876 (1985), Springer
- G. Q. Wang, "A new full Nesterov-Todd step primal-dual path-following interior-point algorithm for symmetric optimization", J. Optim. Theory Appl, 154(3), pp.966~985 (2012)
- G. Q. Wang, "Improved complexity analysis of full Nesterov-Todd step interior-point methods for semidefinite optimization", J. Optim. Theory Appl, 165(1), pp.242~262 (2014)
- G. Q. Wang, "Full Nesterov-Todd step feasible interior-point method for the Cartesian P*(κ)-SCLCP", Optim. Methods Softw, 28(3), pp.600~618 (2013)
- M. Zangiabadi, "Modified polynomial-time full-NT-step in-feasible interior-point algorithm for symmetric optimization", Int. J. Oper. Res.
- L. Zhang, "A full-Newton step interior-point algorithm based on modi ed Newton direction", Oper. Res. Lett, 39(5), pp.318~322 (2011)