@misc{Kiwiel_Krzysztof_A_2006, author={Kiwiel, Krzysztof}, 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 presents a proximal bundle method for constrained convex optimization. It only requires evaluating the problem functions and their subgradients with an unknown accuracy epsilon. Employing a combination of the classic method of centers improvement function with an exact penalty function, it does not need a feasible starting point. It asymptotically finds points with at least ε-optimal objective values that are ε- feasible. When applied to the solution of LP programs via column generation, it allows for ε-accurate solutions of column generation subproblems.}, title={A Method of Centers with Approximate Subgradient Linearizations for Nonsmooth Convex Optimization}, type={Text}, URL={http://rcin.org.pl/Content/139695/PDF/RB-2006-58.pdf}, keywords={Nondifferentiable optimization, Optymalizacja niezróżnicowana, Convex programming, Programowanie wypukłe, Proximal bundle methods, Approximate subgradients, Column generation}, }