Spectral gradient projection method for monotone nonlinear equations with convex constraints

Yu, Zhensheng; Lin, Ji; Sun, Jing; Xiao, Yunhai; Liu, Liying; Li, Zhanhui

doi:10.1016/j.apnum.2009.04.004

Cited by 131 publications

(81 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Numerical results also show that the SPRP method is more efficient and robust than the method in Ref. 7.…”

Section: Introductionmentioning

confidence: 67%

See 1 more Smart Citation

A derivative-free projection method for solving convex constrained monotone equations

Yuan¹

2017

ScienceAsia

View full text Add to dashboard Cite

ABSTRACT:The CG_DESCENT (CGD) method is one of the most efficient conjugate gradient methods for solving unconstrained optimization problems. However, its applications in some other scenarios are relatively few. In this paper, inspired by one spectral PRP projection method, we extend the CGD method, and establish a derivative-free spectral CGD type projection method to solve large-scale nonlinear monotone equations with convex constraints. Due to it inheriting some nice properties of the conjugate gradient method such as the low memory requirement, the proposed method is very suitable to solve large-scale nonlinear monotone equations. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method works well.

show abstract

“…Numerical results also show that the SPRP method is more efficient and robust than the method in Ref. 7.…”

Section: Introductionmentioning

confidence: 67%

“…Yu et al 7 used the above method to solve convex constrained nonlinear monotone equations. They proved that the proposed method is globally convergent under mild assumptions.…”

Section: Introductionmentioning

confidence: 99%

A derivative-free projection method for solving convex constrained monotone equations

Yuan¹

2017

ScienceAsia

View full text Add to dashboard Cite

show abstract

“…In this section, we give the smoothing FR conjugate gradient method for solving (20). Firstly, we give the definition of smoothing function and the smoothing approximation function of the absolute value function; one can see [15,26,27].…”

Section: The Smoothing Fr Conjugate Gradient Methodsmentioning

confidence: 99%

“…And (24) is the smoothing approximation function of (20). Then, problem (20) is solved by smoothing conjugate gradient method.…”

Section: The Smoothing Fr Conjugate Gradient Methodsmentioning

confidence: 99%

“…The absolute value equation can be solved easily now. On the other hand, the conjugate gradient method is suitable for solving large-scare optimization problems and has sample structure and global convergence [19][20][21][22][23][24][25]. In addition, the smoothing methods are used to solve the related nonsmooth optimization problems, such as [26][27][28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with l1-Norm

Chen

2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

We study the method for solving a kind of nonsmooth optimization problems with 1 -norm, which is widely used in the problem of compressed sensing, image processing, and some related optimization problems with wide application background in engineering technology. Transformated by the absolute value equations, this kind of nonsmooth optimization problem is rewritten as a general unconstrained optimization problem, and the transformed problem is solved by a smoothing FR conjugate gradient method. Finally, the numerical experiments show the effectiveness of the given smoothing FR conjugate gradient method.

show abstract

Another hybrid approach for solving monotone operator equations and application to signal processing

Abubakar

Ibrahim

Kura³

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

show abstract

Spectral gradient projection method for monotone nonlinear equations with convex constraints

Cited by 131 publications

References 23 publications

A derivative-free projection method for solving convex constrained monotone equations

A derivative-free projection method for solving convex constrained monotone equations

The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with l1-Norm

Another hybrid approach for solving monotone operator equations and application to signal processing

Contact Info

Product

Resources

About