Nonlinear rescaling vs. smoothing technique in convex optimization
This article is devoted to convex constrained optimization problems. It analyzes the Log-Sigmoid (LS) multipliers method introduced by the author [Ann. Oper. Res. 101, 427-460 (2001; Zbl 0996.90088)]; in particular, it gives a new convergence proof as well as some estimations of the rate of convergence. These results are extended to the case when a modification of the Chen-Harker-Kanzow-Smale smoothing function is used. For Linear Programming problems having a unique dual solution, the LS method is proved to have a global quadratic rate of convergence. The paper reports some numerical results and concludes by listing some topics left for further research.
Chen-Harker-Kanzow-Smale smoothing function
scientific article; zbMATH DE number 1784735