Search

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]

In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization, obtained by a convex combination of the LS and KMD conjugate gradient parameters. A favourite property of the proposed method is that the search direction satisfies the Dai–Liao conjugacy condition and the quasi-Newton direction. In addition, this property does not depend on the line search. Under a modified strong Wolfe line search, we establish the global convergence of the method. Numerical comparison using a set of 109 unconstrained optimization test problems from the CUTEst library show that the proposed method outperforms the Liu–Storey and Hager–Zhang conjugate gradient methods. [ABSTRACT FROM AUTHOR]

In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing. [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]

RMIL conjugate gradient method originally proposed by Rivaie et al. (2012) has recently gained lots of attention. In this article, we propose a generalized conjugate gradient parameter that contains both RMIL and its variant, that is, RMIL+, as special cases. We show that the search direction generated by the new method is sufficiently descent. Under standard mild conditions, we discuss the convergence analysis of the propose method. We demonstrate the numerical efficiency of the propose method on a set of unconstrained minimization benchmark test problems as well as an image restoration problem. The results of the experiment reveal that the proposed method performs better than its main competitors. [ABSTRACT FROM AUTHOR]