Stabilized sequential quadratic programming

Recently, Wright proposed a stabilized sequential quadratic programming alg orithm for inequality constrained optimization. Assuming the Mangasarian-Fr omovitz constraint qualification and the existence of a strictly positive m ultiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic converg ence in cases where both strict complementarity and the Mangasarian-Fromovi tz constraint qualification do not hold. The constraints on the stabilizati on parameter are relaxed, and linear convergence is demonstrated when the p arameter is kept fixed. We show that the analysis of this method can be car ried out using recent results for the stability of variational problems.