Convergence of a splitting inertial proximal method for monotone operators
Journal of Computational and Applied Mathematics
Convergence theorems for inertial KM-type algorithms
Journal of Computational and Applied Mathematics
Asymptotic convergence of an inertial proximal method for unconstrained quasiconvex minimization
Journal of Global Optimization
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We study the asymptotic behavior at infinity of solutions of a second order evolution equation with linear damping and convex potential. The differential system is defined in a real Hilbert space. It is proved that if the potential is bounded from below, then the solution trajectories are minimizing for it and converge weakly towards a minimizer of $\Phi$ if one exists; this convergence is strong when $\Phi$ is even or when the optimal set has a nonempty interior. We introduce a second order proximal-like iterative algorithm for the minimization of a convex function. It is defined by an implicit discretization of the continuous evolution problem and is valid for any closed proper convex function. We find conditions on some parameters of the algorithm in order to have a convergence result similar to the continuous case.