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ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds

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Abstract

This paper presents a descent direction method for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we define a set-valued mapping \(x\rightarrow \partial _{\varepsilon } f(x)\) named ε-subdifferential which is an approximation for the Clarke subdifferential and which generalizes the Goldstein- ε-subdifferential to the Riemannian setting. Using this notion we construct a steepest descent method where the descent directions are computed by a computable approximation of the ε-subdifferential. We establish the global convergence of our algorithm to a stationary point. Numerical experiments illustrate our results.

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  1. ETH Zürich, Seminar for Applied Mathematics, Rämistrasse 101, 8092, Zürich, Switzerland

    P. Grohs & S. Hosseini

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  1. P. Grohs
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  2. S. Hosseini
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Correspondence to S. Hosseini.

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Communicated by: A. Zhou

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Grohs, P., Hosseini, S. ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds. Adv Comput Math 42, 333–360 (2016). https://doi.org/10.1007/s10444-015-9426-z

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