Log-sigmoid multipliers method in constrained optimization

Log-sigmoid multipliers method in constrained optimization

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Article ID: iaor20021390
Country: Netherlands
Volume: 101
Issue: 1
Start Page Number: 427
End Page Number: 460
Publication Date: Jan 2001
Journal: Annals of Operations Research
Authors:
Abstract:

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augmented Lagrangian techniques. We established convergence of the LS type penalty method under very mild assumptions on the input data and estimated the rate of convergence of the LS multipliers method under the standard second order optimality condition for both exact and nonexact minimization. Some important properties of the dual function and the dual problem, which are based on the LS Lagrangian, were discovered and the primal–dual LS method was introduced.

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