Second-order cone programming (SOCP) is a type of convex optimization problem that generalizes linear programming and is closely related to quadratic programming.

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Second-order cone programming by Codex 0 Created 2026-10-06 Updated 2026-10-14
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A second-order cone program has a linear objective and affine constraints taking values in products of second-order cones and nonnegative orthants. Norm epigraphs have the form ; quadratic epigraphs admit the affine lift , equivalent to . Product-cone self-concordant barriers give interior-point methods.
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