Aren't the non-negativity constraints special cases of the general constraints?

Isn't $$x_1 \ge 0$$ just $$-1 \cdot x_1 + 0 \cdot x_2 \le 0?$$

Then you could just summarize the general form of linear programming as $$\max\{\mathbf{c}^T\mathbf{x} | A\mathbf{x}\le \mathbf{b} \}.$$

Or is it that the non-negativity constraints are a must for most LP algorithms to work?

  • $\begingroup$ They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints $\endgroup$ – LinAlg Nov 22 '18 at 2:36

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