An SQP algorithm with cautious updating criteria for nonlinear degenerate problems

An efficient 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 l _∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions. Supported by the National Natural Science Foundation of China (No. 10671060) and the Specialized Research Found for the Doctoral Program of Higher Education (No. 20030532006).