Burachik, R.S.Iusem, A.Melo, J.2025-12-172025-12-172009Journal of Global Optimization, 2009; 46(3):347-3610925-50011573-2916https://hdl.handle.net/1959.8/98124We apply a modified subgradient algorithm (MSG) for solving the dual of anonlinear and nonconvex optimization problem. The dual scheme we consider uses the sharp augmented Lagrangian. A desirable feature of this method is primal convergence, which means that every accumulation point of a primal sequence (which is automatically generated during the process), is a primal solution. This feature is not true in general for available variants of MSG. We propose here two new variants of MSG which enjoy both primal and dual convergence, as long as the dual optimal set is nonempty. These variants have a very simple choice for the step sizes. Moreover, we also establish primal convergence when the dual optimal set is empty. Finally, our second variant of MSG converges in a finite numberof steps.enCopyright 2009 Springernonsmooth optimizationnonconvex optimizationduality schemesharp Lagrangianmodified subgradient algorithm:Journal article10.1007/s10898-009-9429-82-s2.0-77953025852