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Conjugate gradient techniques are known for their simplicity and minimal memory usage. However, it is known that in the vector optimization context, the Polak-Ribi'ere-Polyak (PRP), Liu-Storey (LS), and Hestenes-Stiefel (HS) conjugate gradient (CG) techniques fail to satisfy the sufficient descent property using Wolfe line searches. In this work, we propose a variation of the PRP, LS, and HS CG techniques that we termed YPR, YLS, and YHS, respectively. These techniques exhibit the desirable property of sufficient descent without line search, except for the YHS which uses Wolfe line search for its sufficient descent property. Under certain standard assumptions and employing strong Wolfe conditions, we investigate the global convergence properties of the proposed techniques. The global convergence analysis extends beyond convexity assumption on the objective functions. Additionally, we present numerical experiments and comparisons to demonstrate the implementation, efficiency, and robustness of the proposed techniques. [ABSTRACT FROM AUTHOR]

Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images. [ABSTRACT FROM AUTHOR]