Mixing
Why does the Canonical Form of linear programming have non-negativity?
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
$$max{mathbf{c}^Tmathbf{x} | Amathbf{x}le mathbf{b} }.$$
Or is it that the non-negativity constraints are a must for most LP algorithms to work?
notation linear-programming
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
add a comment |
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
$$max{mathbf{c}^Tmathbf{x} | Amathbf{x}le mathbf{b} }.$$
Or is it that the non-negativity constraints are a must for most LP algorithms to work?
notation linear-programming
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36
add a comment |
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
$$max{mathbf{c}^Tmathbf{x} | Amathbf{x}le mathbf{b} }.$$
Or is it that the non-negativity constraints are a must for most LP algorithms to work?
notation linear-programming
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
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
$$max{mathbf{c}^Tmathbf{x} | Amathbf{x}le mathbf{b} }.$$
Or is it that the non-negativity constraints are a must for most LP algorithms to work?
notation linear-programming
notation linear-programming
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
edited Nov 22 '18 at 21:19
xzhu
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
asked Nov 22 '18 at 0:54
xzhuxzhu
1,9701340
1,9701340
They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36
add a comment |
They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36
They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36
They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36
add a comment |
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They are not a must and your formulation works, but bounds on variables can be handled more efficiently by optimization algorithms than generic constraints
– LinAlg
Nov 22 '18 at 2:36