二阶锥三角函数及其相关公式
Correlation Formulas of Trigonometric Functions Associated with Second-Order Cone

DOI: 10.12677/PM.2016.63031, PP. 199-205

Keywords: 二阶锥，三角函数，相关公式
Second-Order Cone, Trigonometric Functions, Correlation Formulas

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Abstract:

二阶锥函数在求解二阶锥规划及二阶锥互补问题的算法中有广泛应用。本文在约当代数的理论基础上推导得出三角函数在二阶锥上的表达式，然后给出了二阶锥三角函数的若干相关公式。
The function associated with the second-order cones (SOCs) is wildly used in solving second-order cone programming and second-order cone complementarity problems. In this article, on the basis of Euclidean Jordan algebra, the simple formulas of trigonometric functions associated with SOC are derived and some correlation formulas of trigonometric function are also presented.

References

[1]	Faraut, J. and Koranyi, A. (1994) Analysis on Symmetric Cones. Oxford University Press, New York.
[2]	Alizadeh, F. and Goldfarb, D. (2003) Second-Order Cone Programming. Mathematical Programming, 95, 3-15. http://dx.doi.org/10.1007/s10107-002-0339-5
[3]	Chen, J.S., Chen, X. and Tseng, P. (2004) Analysis of Non-smooth Vector-Valued Functions Associated with Sencond- Order Cones. Mathematical Programming, 101, 95-117. http://dx.doi.org/10.1007/s10107-004-0538-3
[4]	Chen, J.S. (2006) The Convex and Monotone Functions Asso-ciated with Second-Order Cone. Optimization, 55, 363- 385. http://dx.doi.org/10.1080/02331930600819514
[5]	Fukushima, M., Luo, Z.Q. and Tseng, P. (2001) Smoothing Functions for Second-Order-Cone Complementarity Problems. SIAM Journal on Control and Optimization, 12, 436-460. http://dx.doi.org/10.1137/S1052623400380365
[6]	罗见今. 论正切数的数学意义及其中西研究史[J]. 内蒙古师范大学学报(自然科学汉文版), 2008, 37(1): 120-124.

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