A descent proximal level bundle method for convex nondifferentiable optimization

We give a proximal level method for convex minimization that uses projections onto successive approximations of level sets of the objective. In contrast to the original level methods of Lemarechal, Nemirovskii and Nesterov, our method is globally convergent without any compactness assumptions and requires bounded storage. It does not employ potentially expensive linesearches as does the level method of Brännlund.