Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing

In this paper, we present two new three-term conjugate gradient methods which can generate sufficient descent directions for the large-scale optimization problems. Note that this property is independent of the line search used. We prove that these three-term conjugate gradient methods are global convergence under the Wolfe line search. Numerical experiments and comparisons demonstrate that the proposed algorithms are efficient approaches for test functions. Moreover, we use the proposed methods to solve the ℓ 1 - α ℓ 2 regularization problem of sparse signal decoding in compressed sensing, and the results show that our methods have certain advantages over the existing solvers on such problems.