Reduced subgradient bundle method for linearly constrained non-smooth non-convex problems

In this paper, we propose an algorithm for solving linearly constrained non-smooth, non-convex optimization problems. The objective functions in these problems are, in general, upper semidifferentiable locally Lipschitz functions. The method is based on the idea of adapting, to the non-smooth setting, the variant of the reduced gradient algorithm proposed by Luenberger, and on bundle techniques which are aimed at building an approximation of the subdifferential. It may be thought of as an extension of reduced gradient methods for dealing with both non-smoothness and non-convexity of the objective function. Under the non-degeneracy assumption, the termination of the proposed algorithm at a stationary point is proved. Numerical results and comparisons with some existing methods are reported to show the efficiency of our algorithm.