The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions
Let \(A\) and \(B\) be two maximal monotone operators on a real Hilbert space \(H\) and let \(\mu, \beta\in (0,\infty).\) This paper is concerned with the convergence analysis of alternating inertial algorithms for inclusion problems of the following type \[ \text{find } (x^*,y^*)\in H\times H \text{ such that } (0,0)\in (I-R+(\beta^{-1}A\times\mu^{-1}B)(x^*,y^*), \] where \(I\) is the identity mapping and \(R: (x,y)\mapsto (y,x).\) The obtained results generalize existing results in the literature. An application to equilibrium problems is also proposed.
scientific article; zbMATH DE number 5704058