Stabilized sequential quadratic programming

Stabilized sequential quadratic programming

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Article ID: iaor20003794
Country: Netherlands
Volume: 12
Issue: 1/2/3
Start Page Number: 253
End Page Number: 273
Publication Date: Jan 1999
Journal: Computational Optimization and Applications
Authors:
Keywords: Quadratic convergence
Abstract:

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

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