Asymptotic convergence of an inertial proximal method for unconstrained quasiconvex minimization (Q1041440)

The spirit of the paper is the same as that in \textit{P. Alvarez}'s paper [SIAM J. Optim. 14, No. 3, 773--782 (2004; Zbl 1079.90096)]. Under conditions related to the involved parameters, relaxation factor and proximal stepsize the author establishes the asymptotic convergence of the inertial and relaxed proximal algorithm for approaching critical points of a smooth and quasiconvex objective function defined on a real Hilbert space. The main results in the paper of \textit{X. Goudou} and \textit{J. Munier} [Math. Program. 116, No. 1--2 (B), 173--191 (2009; Zbl 1151.37326)] are rigorously stated in a new setting , while some of them are improved in either form or requirements of parameters.