The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery

In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.

Automated summary

In 2012, Rivaie et al. proposed the RMIL conjugate gradient (CG) method, which has global convergence under exact line search. However, Dai (2016) discovered convergence abnormalities and introduced restricted RMIL CG parameter as a solution. This paper suggests an efficient RMIL spectral CG method, which does not require additional conditions usually imposed on RMIL. Numerical experiments on benchmark problems and applications in arm robotic model and image restoration demonstrate the promising and efficient performance of the proposed method.