An SQP algorithm with cautious updating criteria for nonlinear degenerate problems
An efficient sequential quadratic programming (SQP) algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the exact penalty function through an Armijo-type line search scheme. This SQP algorithm with cautious update criteria can be considered as a modification of the SQP algorithm given by \textit{J. F. A. de O. Pantoja} and \textit{D. Q. Mayne} [J. Optimization Theory Appl. 69, No. 3, 441--467 (1991; Zbl 0724.90065)]. In the algorithm, the form of quadratic programming subproblem is slightly different from the one given in [loc. cit.], and the update way for the penalty parameter of the used merit function is also different from the usual ways. The global convergence of the algorithm is obtained under the condition of the generalized Mangasarian-Fromvitz constraint qualification. Compared with the previous work [loc. cit.], the boundedness of the solution to the subproblem and the secon-order sufficient condition are not needed. In particular, the algorithm does not need an extra calculation when the iterate point is infesible, which is necessary in the algorithm proposed by \textit{J. Zhang} and \textit{X. Zhang} [Acta Math. Appl. Sin., Engl. Ser. 18, No. 1, 77--84 (2002; Zbl 1114.90480)]. Numerical results indicate that the algorithm is efficient.
scientific article; zbMATH DE number 5632888
scientific article