Stabilized Sequential Quadratic Programming

Authors:
William W. Hager
Affiliations:
Department of Mathematics, University of Florida, Gainesville, FL 32611. hager@math.ufl.edu
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Year:
1999

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Abstract

Recently, Wright proposed a stabilized sequentialquadratic programming algorithm for inequality constrained optimization.Assuming the Mangasarian-Fromovitz constraint qualification andthe existence of a strictly positive multiplier(but possibly dependent constraint gradients), he proved a localquadratic convergence result. In this paper, we establish quadratic convergence in cases whereboth strict complementarity and theMangasarian-Fromovitz constraint qualification do not hold.The constraints on the stabilization parameter are relaxed, and linearconvergence is demonstrated when the parameter is kept fixed.We show that the analysis of this method can be carried out usingrecent results for the stability of variational problems.