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. The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point pa(xk) of xk to define a vk∈∂εkf(pa(xk)) with εk≤α∥vk∥, where α is a constant. The method monitors the reduction in the value of ∥vk∥ to identify when a line search on f should be used. The quasi-Newton step is used to reduce the value of ∥vk∥. Without the differentiability of f, the method converges globally and the rate of convergence is Q-linear. Superlinear convergence is also discussed to extend the characterization result of Dennis and Moré. Numerical results show the good performance of the method.
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Received October 3, 1995 / Revised version received August 20, 1998 Published online January 20, 1999
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Chen, X., Fukushima, M. Proximal quasi-Newton methods for nondifferentiable convex optimization. Math. Program. 85, 313–334 (1999). https://doi.org/10.1007/s101070050059
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DOI: https://doi.org/10.1007/s101070050059