摘要: Recently Bauschke et al. introduced a very interesting and new notion of proximal average in the context convex analysis, studied this subject systemically [3-7] from various viewpoints. In addition, concept was applied to positive semidefinite matrices under name resolvent average, basic properties are successfully established by themselves totally different view techniques analysis rather than classical matrix diagonalization [8]. Inspired their works well-known fact that second-order cone is other typical example symmetric cone, we study on derive corresponding results manner
sci-hub.st 参考文章(9)
Jacques Faraut, Adam Korányi, Analysis on Symmetric Cones ,(1995)
Heinz H. Bauschke, Rafal Goebel, Yves Lucet, Xianfu Wang, The Proximal Average: Basic Theory SIAM Journal on Optimization. ,vol. 19, pp. 766- 785 ,(2008) , 10.1137/070687542
Michel Baes, Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras Linear Algebra and its Applications. ,vol. 422, pp. 664- 700 ,(2007) , 10.1016/J.LAA.2006.11.025
Jein-Shan Chen, The convex and monotone functions associated with second-order cone Optimization. ,vol. 55, pp. 363- 385 ,(2006) , 10.1080/02331930600819514
Heinz H. Bauschke, Xianfu Wang, The kernel average for two convex functions and its application to the extension and representation of monotone operators Transactions of the American Mathematical Society. ,vol. 361, pp. 5947- 5965 ,(2009) , 10.1090/S0002-9947-09-04698-4
Heinz H. Bauschke, Eva Matoušková, Simeon Reich, Projection and proximal point methods: convergence results and counterexamples Nonlinear Analysis-theory Methods & Applications. ,vol. 56, pp. 715- 738 ,(2004) , 10.1016/J.NA.2003.10.010
Heinz H. Bauschke, Yves Lucet, Xianfu Wang, Primal-Dual Symmetric Intrinsic Methods for Finding Antiderivatives of Cyclically Monotone Operators Siam Journal on Control and Optimization. ,vol. 46, pp. 2031- 2051 ,(2007) , 10.1137/060675794
Yves Lucet, Heinz H. Bauschke, Mike Trienis, The piecewise linear-quadratic model for computational convex analysis Computational Optimization and Applications. ,vol. 43, pp. 95- 118 ,(2009) , 10.1007/S10589-007-9124-Y
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang, The resolvent average for positive semidefinite matrices Linear Algebra and its Applications. ,vol. 432, pp. 1757- 1771 ,(2010) , 10.1016/J.LAA.2009.11.028