2016/10/27 by O. P. Ferreira, Ferreira, O. P., S. Z. Németh +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Classical mechanics #Cone (formal languages) #FOS: Mathematics #Lorentz transformation #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Operator (biology) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Order (exchange) #Physics #Piecewise #Piecewise linear function #Pure mathematics #Variational inequality #math.OC
paper · pdf · doi:10.48550/arxiv.1610.08887
openalex publication_date 2016/10/27 · arxiv created 2018/01/19 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The extended second order cones were introduced by S. Z. Németh and G. Zhang in [S. Z. Németh and G. Zhang. Extended Lorentz cones and variational inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for solving mixed complementarity problems and variational inequalities on cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended second order cones. Journal of Global Optimization, 66(3):585-593, 2016] determined the automorphism groups and the Lyapunov or bilinearity ranks of these cones. S. Z. Németh and G. Zhang in [S.Z. Németh and G. Zhang. Positive operators of Extended Lorentz cones. arXiv:1608.07455v2, 2016] found both necessary conditions and sufficient conditions for a linear operator to be a positive operator of an extended second order cone. This note will give formulas for projecting onto the extended second order cones. In the most general case the formula will depend on a piecewise linear equation for one real variable which will be solved by using numerical methods.