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How to project onto extended second order cones

O. P. Ferreira (orizon***at***ufg.br)
S. Z. Németh (s.nemeth***at***bham.ac.uk)

Abstract: 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.

Keywords: Semi-smooth equation, extended second order cone, metric projection, piecewise linear Newton method

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Complementarity and Variational Inequalities

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: November, 2016

Download: [PDF]

Entry Submitted: 11/04/2016
Entry Accepted: 11/04/2016
Entry Last Modified: 11/10/2016

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