A Modified Forward - Backward Splitting Methodfor Maximal Monotone
نویسنده
چکیده
We consider the forward-backward splitting method for nding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modiication to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping is monotone and (Lipschitz) continuous on some closed convex subset of its domain. The modiication entails an additional forward step and a projection step at each iteration. Applications of the modiied method to decomposition in convex programming and monotone variational inequalities are discussed.
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