@misc{Kiwiel_Krzysztof_An_2006, author={Kiwiel, Krzysztof and Lemarechal, Claude}, 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 bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a SIater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient vaIues with unknown accuracy. The proposed approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous - so that 0 is a natural Slater point - and an exact oracle may be time consuming. Finally, this convergence analysis empIoys arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems.}, title={An Inexact Conic Bundle Variant Suited to Column Generation}, type={Text}, URL={http://rcin.org.pl/Content/139723/PDF/RB-2006-55.pdf}, keywords={Nondifferentiable optimization, Optymalizacja niezróżnicowana, Convex programming, Programowanie wypukłe, Proximal bundle methods, Approximate subgradients, Column generation, Aproksymacja subgradientowa, Generowanie kolumn, Cutting-stock problem}, }