Name
Title | ||
|---|---|---|
A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations. |
Abstract | ||
|---|---|---|
It is well known that nonlinear conjugate gradient methods are very effective for large-scale smooth optimization problems. However, their efficiency has not been widely investigated for large-scale nonsmooth problems, which are often found in practice. This paper proposes a modified Hestenes–Stiefel conjugate gradient algorithm for nonsmooth convex optimization problems. The search direction of the proposed method not only possesses the sufficient descent property but also belongs to a trust region. Under suitable conditions, the global convergence of the presented algorithm is established. The numerical results show that this method can successfully be used to solve large-scale nonsmooth problems with convex and nonconvex properties (with a maximum dimension of 60,000). Furthermore, we study the modified Hestenes–Stiefel method as a solution method for large-scale nonlinear equations and establish its global convergence. Finally, the numerical results for nonlinear equations are verified, with a maximum dimension of 100,000. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s10957-015-0781-1 | Journal of Optimization Theory and Applications |
Keywords | Field | DocType |
Nonsmooth, Nonlinear equations, Conjugate gradient, Large scale, Global convergence, 65K05, 90C26 | Conjugate gradient method,Nonlinear system,Mathematical analysis,Nonlinear conjugate gradient method,Optimization problem,Mathematics | Journal |
Volume | Issue | ISSN |
168 | 1 | 1573-2878 |
Citations | PageRank | References |
18 | 0.67 | 46 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gonglin Yuan | 1 | 215 | 13.71 |
| Ze-hong Meng | 2 | 19 | 2.07 |
| Yong Li | 3 | 18 | 0.67 |