对称锥上法锥的图的切锥与法锥描述
Description of Tangent Cone and Normal Cone of the Graph of Normal Cone on Symmetric Cone
摘要: 本文研究了对称锥上法锥的图的切锥和法锥的数学描述。首先,基于对称锥的特性,引入了切锥和法锥的定义。然后,通过构建适当的数学模型,推导出切锥和法锥的精确公式,从而对对称锥规划问题的求解具有重要意义。
Abstract: In this paper, we study the mathematical description of tangent cone and normal cone of the graph of normal cone on symmetric cone. First, the definition of tangent cone and normal cone is introduced based on the properties of the symmetry cone. Then, by constructing appropriate mathematical models, we derive exact formulas for the tangent and normal cones, which have important implications for the solution of the symmetric cone programming problems.
参考文献
|
[1]
|
Goldfarb, D. and Iyengar, G. (2003) Robust Portfolio Selection Problems. Mathematics of Operations Research, 28, 1-38. [Google Scholar] [CrossRef]
|
|
[2]
|
Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994) Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics. [Google Scholar] [CrossRef]
|
|
[3]
|
Vandenberghe, L. and Boyd, S. (1996) Semidefinite Programming. SIAM Review, 38, 49-95. [Google Scholar] [CrossRef]
|
|
[4]
|
Mordukhovich, B.S. (2006) Variational Analysis and Generalized Differentiation, I: Basic Theory. Springer.
|
|
[5]
|
Rockafellar, R.T. and Wets, R.J.B. (1998) Variational Analysis. Springer.
|
|
[6]
|
Faraut, J. and Korányi, A. (1994) Analysis on Symmetric Cones. Oxford University Press.
|
|
[7]
|
Kong, L., Tunçel, L. and Xiu, N. (2010) Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming. Journal of Optimization Theory and Applications, 148, 364-389. [Google Scholar] [CrossRef]
|
|
[8]
|
Wu, J., Zhang, L. and Zhang, Y. (2013) Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions. Set-Valued and Variational Analysis, 22, 155-187. [Google Scholar] [CrossRef]
|