A spectral conjugate gradient projection algorithm to solve the large-scale system of monotone nonlinear equations with application to compressed sensing

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

“…The first inequality directly follows from the Cauchy-Swartz inequality, (32) and the main definition of h k , while the second inequality directly follows from (42) and ( 46). The same result can be shown for the second search direction (24).…”

“…The proposed search directions (15) and (24) satisfy the sufficient descent condition independent of the line-search procedure used.…”

“…The proposed two-direction algorithm was compared to the modified spectral gradient projection (MSGP) algorithm [23] and the derivative-free spectral projection (DFSP) [24]. Furthermore, for the proposed algorithm, we set the starting parameters as follows: a = 0.1, g = 0.0001, c = 0.99, b = 1, and epsilon = 10 −9 .…”

“…Table 1. Numerical comparison of SDYCG algorithm versus DFSP [24], and MSGP algorithms [23]. Moreover, for Problem 3, the proposed algorithm won in terms of the minimum ITER, FEV, and CPU time.…”

“…Figures 1-3 show that, on average, the SDYCG algorithm has less ITER, computing time, and the number of function evaluations than the DFSP and MSGP algorithms. [23], and DFSP [24] for number of iterations. [23], and DFSP [24] for the CPU time.…”