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A descent algorithm for nonsmooth convex optimization

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This paper presents a new descent algorithm for minimizing a convex function which is not necessarily differentiable. The algorithm can be implemented and may be considered a modification of the ε-subgradient algorithm and Lemarechal's descent algorithm. Also our algorithm is seen to be closely related to the proximal point algorithm applied to convex minimization problems. A convergence theorem for the algorithm is established under the assumption that the objective function is bounded from below. Limited computational experience with the algorithm is also reported.

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Fukushima, M. A descent algorithm for nonsmooth convex optimization. Mathematical Programming 30, 163–175 (1984).

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