A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing

Xiao, Yunhai; Zhu, Hong

doi:10.1016/j.jmaa.2013.04.017

Cited by 196 publications

(177 citation statements)

References 17 publications

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“…Note that the continuity in (A2) is weaker than the Lipschitz continuity, which is traditional assumption of methods for solving CCE(F, C), see [3,7,9,17].…”

Section: Preliminariesmentioning

confidence: 99%

“…Since the CCE(F, C) have been used in many applied scientific fields, such as the chemical equilibrium systems [1], the economic equilibrium problems [2], compressive sensing [3], etc., study on numerical methods of (2) has caught much attention from many researchers. For example, based on the proximal decomposition algorithm [4] for variational inequality problems, in [5] Wang et al has proposed an efficient projection method for solving problem (2), and its most important property is that it is free from derivative evaluations.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, too many restarts could slow down the convergence rate. Furthermore, the conjugate gradient type methods in [3,17] are terminated when the temporary point z k satisfies F(z k ) = 0. However, when F(z k ) = 0 we cannot deduce z k is a solution of CCE(F, C) because z k maybe not contained in C. Furthermore, we also cannot deduce F(x k ) = 0 or d k = 0 in this situation.…”

Section: Introductionmentioning

confidence: 99%

“…Then, we describe the new method and prove its global convergence in Sect. 3. Some examples, at last, are presented to show the efficiency of the proposed method.…”

Section: Introductionmentioning

confidence: 99%

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New hybrid conjugate gradient projection method for the convex constrained equations

Sun

Liu

2015

Calcolo

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Based on the two famous Hestenes-Stiefel and Dai-Yuan conjugate gradient methods, a new hybrid conjugate gradient projection method is proposed for the convex constrained equations. At each iteration, the new method is fully free from any derivative evaluations. Furthermore, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Under the condition that the underlying mapping is continuous and monotone, we establish the global convergence of the new method. Compared with traditional methods for solving such problem, our new method does not require the Lipschitz continuity of the underlying mapping. Some large-scale numerical tests are performed and reported, which show that the proposed method is efficient and promising.

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“…Note that the continuity in (A2) is weaker than the Lipschitz continuity, which is traditional assumption of methods for solving CCE(F, C), see [3,7,9,17].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Then, we describe the new method and prove its global convergence in Sect. 3. Some examples, at last, are presented to show the efficiency of the proposed method.…”

Section: Introductionmentioning

confidence: 99%

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New hybrid conjugate gradient projection method for the convex constrained equations

Sun

Liu

2015

Calcolo

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show abstract

“…A prominent feature of these methods is that the search direction does not need gradient information, therefore these methods can be applied for nonsmooth equations. Recently, many numerical methods [3,11,13,14] for nonlinear equations have been presented.…”

Section: Introductionmentioning

confidence: 99%

A modified Liu-Storey conjugate gradient projection algorithm for nonlinear monotone equations

Hu¹,

Wei²

2014

imf

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In this paper, a modified Liu-Storey (LS) conjugate gradient projection algorithm is proposed for solving nonlinear monotone equations based on a hyperplane projection technique. The proposed method is a derivative-free method and can be applied to solving large-scale nonsmooth equations for its lower storage requirement. We can establish its global convergence results under some suitable conditions. Numerical results show that this algorithm is efficient and promising.Mathematics Subject Classification: 65K05, 90C26

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An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

Yuan,

Shao,

Zeng

et al. 2024

Math Methods in App Sciences

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In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.

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A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing

Cited by 196 publications

References 17 publications

New hybrid conjugate gradient projection method for the convex constrained equations

New hybrid conjugate gradient projection method for the convex constrained equations

A modified Liu-Storey conjugate gradient projection algorithm for nonlinear monotone equations

An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

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