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Radu Ioan Bot(radu.botmathematik.tuchemnitz.de) Abstract: We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We propose a forwardbackward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, M.O. Czarnecki and J. Peypouquet in [3]. The condition which guarantees the weak ergodic convergence of the sequence of iterates generated by the proposed scheme is formulated by means of the Fitzpatrick function associated to the maximally monotone operator that describes the set $C$. In the second part we introduce a forwardbackwardforward algorithm for monotone inclusion problems having the same structure, but this time by replacing the cocoercivity hypotheses with Lipschitz continuity conditions. The latter penalty type algorithm opens the gate to handle monotone inclusion problems with more complicated structures, for instance, involving compositions of maximally monotone operators with linear continuous ones. Keywords: maximally monotone operator, Fitzpatrick function, resolvent, cocoercive operator, Lipschitz continuous operator, forwardbackward algorithm, forwardbackwardforward algorithm, subdifferential, Fenchel conjugate Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [PDF] Entry Submitted: 06/03/2013 Modify/Update this entry  
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