Name
Abstract | ||
|---|---|---|
In this paper, we first discuss the geometric properties of the Lorentz cone and the extended Lorentz cone. The self-duality and orthogonality of the Lorentz cone are obtained in Hilbert spaces. These properties are fundamental for the isotonicity of the metric projection with respect to the order, induced by the Lorentz cone. According to the Lorentz cone, the quasi-sublattice and the extended Lorentz cone are defined. We also obtain the representation of the metric projection onto cones in Hilbert quasi-lattices. As an application, solutions of the classic variational inequality problem and the complementarity problem are found by the Picard iteration corresponding to the composition of the isotone metric projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. Our results generalize and improve various recent results obtained by many others. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10957-017-1084-5 | J. Optimization Theory and Applications |
Keywords | Field | DocType |
Lorentz cone, Variational inequality, Metric projection, Complementarity problem, Quasi-lattice, 47H07, 39B62, 47J20, 47H10, 49J40 | Hilbert space,Mathematical optimization,Mathematical analysis,Convex set,Complementarity theory,Dual cone and polar cone,Lorentz transformation,Lorentz covariance,Mathematics,Variational inequality,Velocity-addition formula | Journal |
Volume | Issue | ISSN |
173 | 1 | 1573-2878 |
Citations | PageRank | References |
3 | 0.45 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dezhou Kong | 1 | 3 | 1.13 |
| Lishan Liu | 2 | 188 | 35.41 |
| Yonghong Wu | 3 | 212 | 34.70 |