# Conic program

Jump to: navigation, search

The standard form is

$LaTeX: \min \{ c^T x : Ax=b, \; x \in K\}$,

where $LaTeX: K$ is a cone (not necessarily convex). This is more general than it looks. Suppose $LaTeX: S$ is any non-empty set, and we have the mathematical program:

$LaTeX: \min \{ c^T x : x \in S\}$.

Then, defining $LaTeX: K = \{t(1,x): x \in S, \; t \ge 0\}$, we have that the above problem is equivalent to the conic program:

$LaTeX: \min \{ c^Tx : (x_0, x) \in K, \; x_0 = 1 \}$.

This problem class also includes the semi-definite program, as $LaTeX: x$ could be a matrix.