Just as the title suggests, what is the geometric representation of a MISOCP? I know a SOCP can be geometrically (or visually) described as a cone... what about a mixed integer second order cone program in a low dimensional space (like 3D)?
2026-02-22 21:57:37.1771797457
What is the geometric representation of a mixed integer second order cone program?
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The mixed-integer prefix means simply that in your set some coordinates are restricted to be integers. For example this MISOCP
$$ \begin{array}{l} x\geq \sqrt{y^2+z^2} \\ x = r \\ y,z\in\mathbb{Z} \end{array} $$
describes the set of lattice points in a disk of radius $r$.