|
|
Pure Mathematics 2020
一类可变盒子上投影算子的几何性质研究
|
Abstract:
闭凸锥投影算子几何性质对增广拉格朗日方法，投影算子几何性质的研究以及优化问题的灵敏性分析有着至关重要的作用。本文研究一类可变盒子的对偶锥、切锥、极锥与临界锥为进一步研究这一类可变盒子上投影算子的几何性质以及相关优化问题的灵敏度分析奠定了基础。
The geometric properties of closed convex cone projection operators are very important for the study of Lagrangian, the geometric properties of projection operators and the sensitivity analysis of optimization problems. In this paper, we study the dual cone, tangent cone, polar cone and critical cone of a class of variable box, which lays a foundation for the further study of the geometric properties of projection operators on this class of variable box and the sensitivity analysis of related optimization problems.
| [1] | Sun, D.F. (2006) The Strong Second Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semide？nite Programming and Their Implications. Mathematics of Operations Research, 31, 649-848. https://doi.org/10.1287/moor.1060.0195 |
| [2] | Wu, B., Ding, C., Sun, D.F., et al. (2014) On the Moreau-Yoshida Regularization of the Vector K-Norm Related Functions. SIAM Journal on Optimization, 24, 766-794. https://doi.org/10.1137/110827144 |
| [3] | Clarke, F.H. (1990) Optimization and Nonsmooth Analysis. John Wiley and Sons, New York, Chapter 2, Generalized Gradients, 50-62. |
| [4] | Liu, Y.J., Wang, S.Y. and Sun, J.H. (2013) Find-ing the Projection onto the Intersection of a Closed Half-Space and a Variable Box. Operations Research Letters, 41, 259-264. https://doi.org/10.1016/j.orl.2013.01.014 |
| [5] | Wang, S.Y. and Zhang, Q.Y. (2018) Variational Geo-metric Properties of Two Classes of Closed Convex Cones. Journal of Shenyang Aerospace University, 35, 93-96. |
| [6] | Hu, X., Liu, Y.J., Liu, M.J. and Gao, J.R. (2013) Study on the Projection Operator over the Set of Variable Box. Journal of Shenyang Aerospace University, 30, 93-96. |
| [7] | Han, N., Liu, Y.J. and Liu, M.J. (2013) Computation of the Metric Projection over a Class of Closed Convex Cones. Journal of Shenyang Aerospace University, 30, 88-91. |
