# LP and SDP nomenclature

A canonical form of primal linear program is $$\text{minimize } c^T \cdot x \\ \text{subject to } Ax = b, x \geq 0$$

The dual is $$\text{maximize } b^T \cdot y \\ \text{subject to } z \equiv c - A^T y \geq 0$$

As far as I know $y$ are called Lagrange multipliers. How do you refer to the other terms, i.e. $A,b,c,x$ and $z$ in LP (and SDP)?

$x$ is primal variable, $y$ is dual variable ($y$ is usually not referred to as Lagrange multiplier unless you form Lagrangian explicitly).
Others are usually referred by symbol directly rather than name, the linear coefficient ($c$), linear constraint matrix ($A$), right-hand-side of linear constraint ($b$).
If you have quadratic term $x^\top Hx$, then $H$ is the quadratic matrix or the Hessian
• $z$ is often referred to as the "dual slack variable(s)" – Brian Borchers Jun 18 '15 at 16:24