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A descent algorithm for nonsmooth convex optimization
Authors:Masao Fukushima
Affiliation:(1) Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 606 Kyoto, Japan
Abstract: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.
Keywords:Nonsmooth Optimization  Subgradient  ε  -Subdifferential  Descent Method  Cutting Planes
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