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A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization

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  • Jian, Jin-Bao
  • Pan, Hua-Qin
  • Tang, Chun-Ming
  • Li, Jian-Ling

Abstract

In this paper, a primal-dual quasi interior-point algorithm for inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The algorithm starts from an arbitrarily initial point. Then after finite iterations, the iteration points enter into the interior of the feasible region and the objective function is monotonically decreasing. Furthermore, the proposed algorithm is proved to possess global and superlinear convergence under mild conditions including a weak assumption of positive definiteness. Finally, some encouraging preliminary computational results are reported.

Suggested Citation

  • Jian, Jin-Bao & Pan, Hua-Qin & Tang, Chun-Ming & Li, Jian-Ling, 2015. "A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 560-578.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:560-578
    DOI: 10.1016/j.amc.2015.05.091
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    References listed on IDEAS

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    1. J. B. Jian, 2006. "New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 109-130, April.
    2. Z. Y. Gao & G. P. He & F. Wu, 1997. "Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 371-397, November.
    3. Jian, Jin-Bao & Tang, Chun-Ming & Zheng, Hai-Yan, 2010. "Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 645-657, February.
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    Cited by:

    1. Li, Jianling & Yang, Zhenping, 2018. "A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 52-72.
    2. Li, Jianling & Huang, Renshuai & Jian, Jinbao, 2015. "A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 885-903.

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