Second-order cone programming
= Second-order cone programming
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= Second-order cone program
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= SOCP
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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 $(t,z)\in\mathcal Q$; quadratic epigraphs admit the affine lift $((q+1)/2,(q-1)/2,a)\in\mathcal Q_3$, equivalent to $q\geq a^2$. Product-cone <self-concordant barriers> give <interior-point methods>.