Abstract
Given a maximal monotone operator T,we consider a certain ε-enlargement T ε, playing the role of the ε-subdifferential in nonsmooth optimization. We establish some theoretical properties of T ε, including a transportation formula, its Lipschitz continuity, and a result generalizing Brønsted & Rockafellar’s theorem. Then we make use of the ε-enlargement to define an algorithm for finding a zero of T.
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Burachik, R.S., Sagastizábal, C.A., Svaiter, B.F. (1998). ε-Enlargements of Maximal Monotone Operators: Theory and Applications. In: Fukushima, M., Qi, L. (eds) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Applied Optimization, vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6388-1_2
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DOI: https://doi.org/10.1007/978-1-4757-6388-1_2
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