We present a new spectral conjugate gradient method based on the Dai-Yuan
strategy to solve large-scale unconstrained optimization problems with
applications to compressive sensing. In our method, the numerator of
conjugate gradient parameter is a convex combination from the maximum
gradient norm value in some preceding iterates and the current gradient norm
value. This combination will try to produce the larger step-size far away
from the optimizer and the smaller step-size close to it. In addition, the
spectral parameter guarantees the descent property of the new generated
direction in each iterate. The global convergence results are established
under some standard assumptions. Numerical results are reported which
indicate the promising behavior of the new procedure to solve large-scale
unconstrained optimization and compressive sensing problems.
Large-scale sparse reconstruction through partitioned compressive sensing
