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

作者：Jian, JB^*; Tang, CM; Hu, QJ; Zheng, HY

来源：Journal of Computational and Applied Mathematics, 2005, 180(2): 391-412.

DOI：10.1016/j.cam.2004.11.008

• general constrained optimization
• SQP
• feasible descent algorithm
• superlinear convergence
• strict complementarity

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.

• 出版日期2005-8-15
• 单位广西大学