An inexact bundle variant suited to column generation (Q1016116)

The authors give a bundle method for constrained convex optimization of the form \[ \text{inf\,}f(u),\quad u\in\mathbb{C},\quad h(u)\leq 0, \] where \(\mathbb{C}\) is a simple closed convex set in the Euclidean space, \(f\) is a simple convex real-valued function and \(h\) is also a convex real-valued function. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. The given method is illustrated on a number of cutting-stock problems.