A proximal quasi-Newton method based on memoryless modified symmetric rank-one formula

We consider proximal gradient methods for minimizing a composite function of differentiable and convex function. To accelerate the general methods, we focus on quasi-Newton type based mappings scaled by matrices. Although it is usually difficult to compute mappings, applying memoryless symmetric rank-one (SR1) formula makes this easier. Since (quasi-Newton) matrices must be positive definite, develop an algorithm using SR1 modified spectral scaling secant condition. give subsequential convergence property proposed method objective functions. In addition, show R-linear under strong convexity assumption. Finally, some numerical results are reported.