A DESCENT PROXIMAL LEVEL BUNDLE METHOD FOR CONVEX NONDIFFERENTIABLE OPTIMIZATION

We give a proximal level method for convex minimization that uses proj ections 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 compactnes s assumptions and requires bounded storage. It does not employ potenti ally expensive linesearches as does the level method of Brannlund.