A feasible descent SQP algorithm for general constrained optimization without strict complementarity

  • Authors:

  • Jin-Bao Jian;Chun-Ming Tang;Qing-Jie Hu;Hai-Yan Zheng

  • Affiliations:

  • College of Mathematics and Information Science, Guangxi University, 530004, Nanning, PR China;College of Mathematics and Information Science, Guangxi University, 530004, Nanning, PR China;College of Mathematics and Information Science, Guangxi University, 530004, Nanning, PR China;College of Mathematics and Information Science, Guangxi University, 530004, Nanning, PR China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

In this paper, a class of optimization problems with equality and inequality constraints is discussed. Firstly, the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter. The later problem is shown to be equivalent to the original problem if the parameter is large enough (but finite), then a feasible descent SQP algorithm for the simplified problem is presented. At each iteration of the proposed algorithm, a master direction is obtained by solving a quadratic program (which always has a feasible solution). With two corrections on the master direction by two simple explicit formulas, the algorithm generates a feasible descent direction for the simplified problem and a height-order correction direction which can avoid the Maratos effect without the strict complementarity, then performs a curve search to obtain the next iteration point. Thanks to the new height-order correction technique, under mild conditions without the strict complementarity, the globally and superlinearly convergent properties are obtained. Finally, an efficient implementation of the numerical experiments is reported.