@misc{Kiwiel_Krzysztof_A_2004, author={Kiwiel, Krzysztof}, copyright={Creative Commons Attribution BY 4.0 license}, address={Warszawa}, journal={Raport Badawczy = Research Report}, howpublished={online}, year={2004}, publisher={Instytut BadaƄ Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, abstract={The paper presents a proximal bundle method for minimizing a convex function f over a closed convex set. It only requires evaluating f and its subgradients with an accuracy e > 0, which is fixed but possibly unknown. It asymptotically finds points that are e-optimal. When applied to Lagrangian relaxation, it allows for e-accurate solutions of Lagrangian subproblems, and finds e-optimal solutions of convex programs.}, title={A Proximal Bundle Method with Approximate Subgradient Linearizations}, type={Text}, URL={http://rcin.org.pl/Content/139602/PDF/RB-2004-65.pdf}, keywords={Nondifferentiable optimization, Lagrangian relaxation, Convex programming, Proximal bundle methods, Approximate subgradients}, }