A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization

Li, Ming; Liu, Hongwei; Liu, Zexian

doi:10.1007/s11075-017-0434-6

Cited by 18 publications

(22 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The relation (17) provides a proper estimation that is (15) for the g T k+1 B k+1 g k+1 . Basically, the essence of the idea of Li et al (2018) is to approximate the Hessian by the matrix (s T k y k / s k 2 )I or ( y k 2 /s T k y k )I . (18) might imply that approximation Hessian matrix possesses suitable condition numbers, and the y k 2 s T k y k contained in K 1 conserves the positive definiteness of A k+1 together with ρ k+1 > 0.…”

Section: Conic Modelmentioning

confidence: 99%

“…Actually, it is observed by Raydan (1997) that the BB gradient method is desirable to the typical gradient method. Therefore, when the search direction is negative gradient direction, we first take the following choice (Li et al 2018):…”

Section: Choices Of the Initial Stepsizementioning

confidence: 99%

“…Inspired by SMCG and BBCG, Liu and Liu (2018a) presented an efficient Barzilai-Borwein conjugate gradient method (SMCG_BB) with the generalized Wolfe line search for unconstrained optimization. Li et al (2018) extended the approach to the three-dimensional subspace minimization conjugate gradient method for solving the unconstrained optimization problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

Liu

2019

Comp. Appl. Math.

Self Cite

View full text Add to dashboard Cite

In this paper, we present a new conjugate gradient method, in which the search direction is computed by minimizing a selected approximate model in a two-dimensional subspace. That is, if the objective function is not close to a quadratic, the search direction is generated by a conic model. Otherwise, a quadratic model is considered. The direction of the proposed method is proved to possess the sufficient descent property. With the modified nonmonotone line search, we establish a global convergence of the proposed method under appropriate assumptions. R-linear convergence of the proposed method is also analyzed. Numerical results using two different test function collections show that the proposed algorithm is efficient.

show abstract

Section: Conic Modelmentioning

confidence: 99%

Section: Choices Of the Initial Stepsizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

Liu

2019

Comp. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The next theorems are also given in [62]. (13), then the scaling parameters given by (57) and (58) are the unique global solutions of the problem (56). Theorem 1.2.12.…”

Section: Applied Mathematicsmentioning

confidence: 99%

“…Theorem 1.2.12. Let δ k be computed by (57). Then, for any k ¼ 0, 1, …, δ k is positive and close to 1.…”

Section: Applied Mathematicsmentioning

confidence: 99%

Some Unconstrained Optimization Methods

Djordjević¹

2019

Applied Mathematics

View full text Add to dashboard Cite

Although it is a very old theme, unconstrained optimization is an area which is always actual for many scientists. Today, the results of unconstrained optimization are applied in different branches of science, as well as generally in practice. Here, we present the line search techniques. Further, in this chapter we consider some unconstrained optimization methods. We try to present these methods but also to present some contemporary results in this area.

show abstract

A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

Sun

Liu

2021

J Optim Theory Appl

View full text Add to dashboard Cite

A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization

Cited by 18 publications

References 33 publications

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

Some Unconstrained Optimization Methods

A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

Contact Info

Product

Resources

About