Name
Title | ||
|---|---|---|
On the convergence properties of non-Euclidean extragradient methods for variational inequalities with generalized monotone operators |
Abstract | ||
|---|---|---|
In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing approximate strong solutions of these problems, and demonstrate how their iteration complexities depend on the global Lipschitz or Hölder continuity properties for their operators and the smoothness properties for the distance generating function used in the N-EG algorithms. We also introduce a variant of this algorithm by incorporating a simple line-search procedure to deal with problems with more general continuous operators. Numerical studies are conducted to illustrate the significant advantages of the developed algorithms over the existing ones for solving large-scale GMVI problems. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s10589-014-9673-9 | Computational Optimization and Applications |
Keywords | Field | DocType |
Complexity,Monotone variational inequality,Pseudo-monotone variational inequality,Extragradient methods,Non-Euclidean methods,Prox-mapping | Convergence (routing),Generating function,Mathematical optimization,Mathematical analysis,Lipschitz continuity,Hölder condition,Operator (computer programming),Smoothness,Mathematics,Monotone polygon,Variational inequality | Journal |
Volume | Issue | ISSN |
60 | 2 | 0926-6003 |
Citations | PageRank | References |
9 | 0.58 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cong D. Dang | 1 | 28 | 1.42 |
| Guanghui Lan | 2 | 1212 | 66.26 |