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A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

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Abstract

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.

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Authors and Affiliations

  1. College of Mathematics and Informatics Science, Guangxi University, 530004, Nanning, People’s Republic of China

    Jin-bao Jian, Chun-ming Tang & Hai-yan Zheng

  2. Department of Information, Hunan Business College, 410205, Changsha, People’s Republic of China

    Qing-jie Hu

  3. Institute of Applied Mathematics, Hunan University, 410082, Changsha, People’s Republic of China

    Qing-jie Hu

Authors
  1. Jin-bao Jian
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  2. Qing-jie Hu
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  3. Chun-ming Tang
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  4. Hai-yan Zheng
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Corresponding author

Correspondence to Jin-bao Jian.

Additional information

Project supported by the National Natural Science Foundation (No. 10261001), Guangxi Science Foundation (Nos. 0236001, 064001), and Guangxi University Key Program for Science and Technology Research (No. 2005ZD02) of China.

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Jian, Jb., Hu, Qj., Tang, Cm. et al. A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions. Appl Math Optim 56, 343–363 (2007). https://doi.org/10.1007/s00245-007-9010-0

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