A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm

Abstract

In this note, an inertial and relaxed version of a diagonal hybrid projection-proximal point algorithm is considered, in order to find the minimum of a function f approximated by a sequence of functions (in general, smoother than f or taking into account some constraints of the problem). Two convergence theorems are proved under different kind of assumptions, which allows to apply the method in various cases.

Keywords::

• parametric approximation
• diagonal iteration
• proximal point
• hybrid method
• inertial term
• relaxation
• global convergence

AMS Subject Classifications::

• Primary: 90C25; 65K05; Secondary: 49M30; 90C51

Acknowledgements

M. Carrasco was partially supported by FONDECYT grant 3080037. K. Pichard was supported by ECOS/CONICYT. The authors wish to thank the Centro de Modelamiento Matemático where part of this research was carried out.