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t\in \mathbb{R}, ||x||_2\leq t \right\}</math>.
The second-order cone is also known by '''quadratic cone''' or '''ice-cream cone''' or '''Lorentz cone'''. The standard second-order cone in <math>\mathbb{R}^3</math> is <math>\left\{(x,y,z) \Big| \sqrt{x^2 + y^2} \leq z \right\}</math>.
The set of points satisfying a second-order cone constraint is the inverse image of the unit second-order cone under an affine mapping:
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