An efficient modified conjugate gradient algorithm under Wolfe conditions with applications in compressive sensing

This paper presents a new modified conjugate gradient (NMCG) algorithm which satisfies the sufficient descent property under any line search for unconstrained optimization problems. We analyze that the algorithm is global convergence under the Wolfe line search. We use the proposed algorithm NMCG to unconstrained optimization problems to prove its effectiveness. Furthermore, we also extend it to solve image restoration and sparse signal recovery problems in compressive sensing, and the results indicate that our algorithm is effective and competitive.