Mixing
How get the extreme directions of an unbounded feasible region
$begingroup$
The following constraints form a feasible region.
$-x_1+x_2 le 2$
$-x_1+2x_2 le 6$
$x_1,x_2 ge 0$
The feasible region have three extreme points: $e_1=left[begin{array}{cc}
0\
0
end{array}right]$ $e_2=left[begin{array}{cc}
0\
2
end{array}right]$ $e_3=left[begin{array}{cc}
2\
4
end{array}right]$
What is the procedure that I need to follow to extract the extreme direction from this data?
Extrene Direction: An extreme direction of a convex set is a direction of the set that cannot be represented as a positive combination of two distinct directions of the set.
linear-programming
asked Jan 23 at 14:03
user637533user637533
83
$endgroup$
add a comment |
$begingroup$
The following constraints form a feasible region.
$-x_1+x_2 le 2$
$-x_1+2x_2 le 6$
$x_1,x_2 ge 0$
The feasible region have three extreme points: $e_1=left[begin{array}{cc}
0\
0
end{array}right]$ $e_2=left[begin{array}{cc}
0\
2
end{array}right]$ $e_3=left[begin{array}{cc}
2\
4
end{array}right]$
What is the procedure that I need to follow to extract the extreme direction from this data?
Extrene Direction: An extreme direction of a convex set is a direction of the set that cannot be represented as a positive combination of two distinct directions of the set.
linear-programming
asked Jan 23 at 14:03
user637533user637533
83
$endgroup$
$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03
add a comment |
$begingroup$
The following constraints form a feasible region.
$-x_1+x_2 le 2$
$-x_1+2x_2 le 6$
$x_1,x_2 ge 0$
The feasible region have three extreme points: $e_1=left[begin{array}{cc}
0\
0
end{array}right]$ $e_2=left[begin{array}{cc}
0\
2
end{array}right]$ $e_3=left[begin{array}{cc}
2\
4
end{array}right]$
What is the procedure that I need to follow to extract the extreme direction from this data?
Extrene Direction: An extreme direction of a convex set is a direction of the set that cannot be represented as a positive combination of two distinct directions of the set.
linear-programming
asked Jan 23 at 14:03
user637533user637533
83
$endgroup$
The following constraints form a feasible region.
$-x_1+x_2 le 2$
$-x_1+2x_2 le 6$
$x_1,x_2 ge 0$
The feasible region have three extreme points: $e_1=left[begin{array}{cc}
0\
0
end{array}right]$ $e_2=left[begin{array}{cc}
0\
2
end{array}right]$ $e_3=left[begin{array}{cc}
2\
4
end{array}right]$
What is the procedure that I need to follow to extract the extreme direction from this data?
Extrene Direction: An extreme direction of a convex set is a direction of the set that cannot be represented as a positive combination of two distinct directions of the set.
linear-programming
linear-programming
asked Jan 23 at 14:03
user637533user637533
83
asked Jan 23 at 14:03
user637533user637533
83
edited Jan 23 at 19:02
user637533
asked Jan 23 at 14:03
user637533user637533
83
asked Jan 23 at 14:03
user637533user637533
83
asked Jan 23 at 14:03
user637533user637533
83
83
$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03
add a comment |
$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03
$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03
add a comment |
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$begingroup$
the costraints equations with the term on the right 0 and with "=" instead of $le$.
$endgroup$
– tommycautero
Jan 23 at 14:07
$begingroup$
What do you mean by "extreme directions" in this context?
$endgroup$
– callculus
Jan 23 at 18:38
$begingroup$
Check the edit that I've done
$endgroup$
– user637533
Jan 23 at 19:03