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Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions

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  • Jian, Jin-Bao
  • Tang, Chun-Ming
  • Zheng, Hai-Yan

Abstract

In this paper, we present a sequential quadratically constrained quadratic programming (SQCQP) norm-relaxed algorithm of strongly sub-feasible directions for the solution of inequality constrained optimization problems. By introducing a new unified line search and making use of the idea of strongly sub-feasible direction method, the proposed algorithm can well combine the phase of finding a feasible point (by finite iterations) and the phase of a feasible descent norm-relaxed SQCQP algorithm. Moreover, the former phase can preserve the "sub-feasibility" of the current iteration, and control the increase of the objective function. At each iteration, only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction. Without any other correctional directions, the global, superlinear and a certain quadratic convergence (which is between 1-step and 2-step quadratic convergence) properties are proved under reasonable assumptions. Finally, some preliminary numerical results show that the proposed algorithm is also encouraging.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:645-657
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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. M. V. Solodov, 2004. "On the Sequential Quadratically Constrained Quadratic Programming Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 64-79, February.
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    Cited by:

    1. Tang, Chun-ming & Jian, Jin-bao, 2012. "Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions," European Journal of Operational Research, Elsevier, vol. 218(1), pages 28-37.
    2. Jin-bao Jian & Xing-de Mo & Li-juan Qiu & Su-ming Yang & Fu-sheng Wang, 2014. "Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 158-188, January.
    3. 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.
    4. 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.

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