Conic optimization

Conic optimization is a subfield of convex optimization that studies a class of structured convex optimization problems called conic optimization problems. A conic optimization problem consists of minimizing a convex function over the intersection of an affine subspace and a convex cone.

The class of conic optimization problems is a subclass of convex optimization problems and it includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.

Given a real vector space X, a convex, real-valued function

defined on a convex cone ${\displaystyle C\subset X}$, and an affine subspace ${\displaystyle {\mathcal {H}}}$ defined by a set of affine constraints ${\displaystyle h_{i}(x)=0\ }$, a conic optimization problem is to find the point ${\displaystyle x}$ in ${\displaystyle C\cap {\mathcal {H}}}$ for which the number ${\displaystyle f(x)}$ is smallest.

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