Polyak, Roman A. Log-sigmoid multipliers method in constrained optimization. (English) Zbl 0996.90088 Ann. Oper. Res. 101, 427-460 (2001). 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. 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. Cited in 1 ReviewCited in 26 Documents MSC: 90C46 Optimality conditions and duality in mathematical programming 49N15 Duality theory (optimization) 90C30 Nonlinear programming Keywords:log-sigmoid; multipliers method; duality; smoothing technique PDFBibTeX XMLCite \textit{R. A. Polyak}, Ann. Oper. Res. 101, 427--460 (2001; Zbl 0996.90088) Full Text: DOI