Abstract
To find a zero of a maximal monotone operator T we use an enlargement T ε playing the role of the ε-subdifferential in nonsmooth optimization. We define a convergent and implementable algorithm which combines projection ideas with bundle-like techniques and a transportation formula. More precisely, first we separate the current iterate x k from the zeros of T by computing the direction of minimum norm in a polyhedral approximation of T ε k(x k). Then suitable elements defining such polyhedral approximations are selected following a bundle strategy. Finally, the next iterate is computed by projecting x k onto the corresponding separating hyperplane.
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Burachik, R.S., Sagastizábal, C., Svaiter, B.F. (1999). Bundle Methods for Maximal Monotone Operators. In: Théra, M., Tichatschke, R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45780-7_4
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DOI: https://doi.org/10.1007/978-3-642-45780-7_4
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