Linear convergence of the generalized PPA and several splitting methods for the composite inclusion problem

摘要: For the inclusion problem involving two maximal monotone operators, under metric subregularity of composite operator, we derive linear convergence generalized proximal point algorithm and several splitting algorithms, which include over-relaxed forward-backward algorithm, Douglas-Rachford Davis' three-operator algorithm. To best our knowledge, this condition is weaker than existing ones that almost all require strong monotonicity operator. Withal, give some sufficient conditions to ensure At last, preliminary numerical performances on toy examples support theoretical results.