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Zbl 0996.90088
Polyak, Roman A.
Log-sigmoid multipliers method in constrained optimization. (English)
[J] Ann. Oper. Res. 101, 427-460 (2001). ISSN 0254-5330; ISSN 1572-9338/e

Summary: 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. \par 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. \par 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.

MSC 2000:: *90C46 Optimality conditions, duality
49N15 Duality theory (optimization)
90C30 Nonlinear programming

Keywords: log-sigmoid; multipliers method; duality; smoothing technique

Cited in: Zbl 1022.90014

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