An inexact conic bundle variant suited to column generation

摘要: We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way Slater point, assumed to be known. Besides, the accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated number applications in column generation, which constraints are positively homogeneous -- so that 0 natural point exact may time consuming. Finally, our convergence analysis employs arguments have been little used far community. The illustrated on cutting-stock problems.