@misc{Kiwiel_Krzysztof_Lagrangian_2006,
 author={Kiwiel, Krzysztof and Larsson, Torbjörn and Lindberg, Per},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2006},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={The paper demonstrates useful properties of ballstep subgradient methods for convex optimization that use level controls for estimating the optimal value. Augmented with simple averaging schemes, they asymptotically find objective and constraint subgradients involved in optimality conditions. When applied to Lagrangian relaxation of convex programs, they find both primal and dual solutions, and have practicable stopping criteria. Up till now, similar results have only been known for proximal bundle methods, and for subgradient methods with divergent series stepsizes, whose convergence can be slow. Encouraging numerical results are presented for large-scale nonlinear multicommodity network flow problems.},
 title={Lagrangian Relaxation via Ballstep Subgradient Methods},
 type={Text},
 URL={http://rcin.org.pl/Content/139731/PDF/RB-2006-57.pdf},
 keywords={Nondifferentiable optimization, Optymalizacja niezróżnicowana, Lagrangian relaxation, Convex programming, Programowanie wypukłe, Level projection methods, Subgradient optimization, Relaksacja lagrange'a},
}