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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)?

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$x$ 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

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    $\begingroup$ $z$ is often referred to as the "dual slack variable(s)" $\endgroup$ – Brian Borchers Jun 18 '15 at 16:24

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