Set of Feasible DirectionsAre these solutions to a LP problem feasible? basic?Construct a linear programming problem for which both the primal and the dual problem has no feasible solutionFinding all basic feasible solutions in a linear programWhat's a basic solution, and how do we find them?How can I determine feasability / optimality given a set of variables?Why feasible set of LP is a polyhedronBasic solution, basic feasible solution, degeneracyExtreme directions of $S=x:-x_1+2x_2le 4,x_1-3x_2le 3,x_1,x_2ge 0$Finding cones of directionsHow to find an extreme feasible point in a linear polytope (set $x : Ax leq b$ defined by halfspaces)?
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Set of Feasible Directions
Are these solutions to a LP problem feasible? basic?Construct a linear programming problem for which both the primal and the dual problem has no feasible solutionFinding all basic feasible solutions in a linear programWhat's a basic solution, and how do we find them?How can I determine feasability / optimality given a set of variables?Why feasible set of LP is a polyhedronBasic solution, basic feasible solution, degeneracyExtreme directions of $S=x:-x_1+2x_2le 4,x_1-3x_2le 3,x_1,x_2ge 0$Finding cones of directionsHow to find an extreme feasible point in a linear polytope (set $x : Ax leq b$ defined by halfspaces)?
$begingroup$
I don't even know what to do for the first part. How do you even find all the feasible directions of a particular Set...?
Then how do you proceed to finding basic directions?
linear-programming
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
$endgroup$
add a comment |
$begingroup$
I don't even know what to do for the first part. How do you even find all the feasible directions of a particular Set...?
Then how do you proceed to finding basic directions?
linear-programming
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
$endgroup$
$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10
add a comment |
$begingroup$
I don't even know what to do for the first part. How do you even find all the feasible directions of a particular Set...?
Then how do you proceed to finding basic directions?
linear-programming
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
$endgroup$
I don't even know what to do for the first part. How do you even find all the feasible directions of a particular Set...?
Then how do you proceed to finding basic directions?
linear-programming
linear-programming
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
asked Nov 27 '15 at 1:02
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
3419
3419
$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10
add a comment |
$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10
$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10
$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Use the definition of a feasible direction $d$ at $(0,0,1)$: $(0,0,1)+theta din P$ for all $thetain (0,delta)$ for some $delta>0$ if and only if $theta d_1 +theta d_2 +1+theta d_3=1$ and $theta d_1geq 0$, $theta d_2geq 0$ and $1+theta d_3geq 0$ for all $thetain (0,delta)$. Since $thetain (0,delta)$, this is equivalent to $$d_1+d_2+d_3=0,quad d_1,d_2geq 0,quad theta d_3geq -1$$ for all $thetain (0,delta)$. This defines the feasible directions.
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Use the definition of a feasible direction $d$ at $(0,0,1)$: $(0,0,1)+theta din P$ for all $thetain (0,delta)$ for some $delta>0$ if and only if $theta d_1 +theta d_2 +1+theta d_3=1$ and $theta d_1geq 0$, $theta d_2geq 0$ and $1+theta d_3geq 0$ for all $thetain (0,delta)$. Since $thetain (0,delta)$, this is equivalent to $$d_1+d_2+d_3=0,quad d_1,d_2geq 0,quad theta d_3geq -1$$ for all $thetain (0,delta)$. This defines the feasible directions.
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
$endgroup$
add a comment |
$begingroup$
Use the definition of a feasible direction $d$ at $(0,0,1)$: $(0,0,1)+theta din P$ for all $thetain (0,delta)$ for some $delta>0$ if and only if $theta d_1 +theta d_2 +1+theta d_3=1$ and $theta d_1geq 0$, $theta d_2geq 0$ and $1+theta d_3geq 0$ for all $thetain (0,delta)$. Since $thetain (0,delta)$, this is equivalent to $$d_1+d_2+d_3=0,quad d_1,d_2geq 0,quad theta d_3geq -1$$ for all $thetain (0,delta)$. This defines the feasible directions.
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
$endgroup$
add a comment |
$begingroup$
Use the definition of a feasible direction $d$ at $(0,0,1)$: $(0,0,1)+theta din P$ for all $thetain (0,delta)$ for some $delta>0$ if and only if $theta d_1 +theta d_2 +1+theta d_3=1$ and $theta d_1geq 0$, $theta d_2geq 0$ and $1+theta d_3geq 0$ for all $thetain (0,delta)$. Since $thetain (0,delta)$, this is equivalent to $$d_1+d_2+d_3=0,quad d_1,d_2geq 0,quad theta d_3geq -1$$ for all $thetain (0,delta)$. This defines the feasible directions.
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
$endgroup$
Use the definition of a feasible direction $d$ at $(0,0,1)$: $(0,0,1)+theta din P$ for all $thetain (0,delta)$ for some $delta>0$ if and only if $theta d_1 +theta d_2 +1+theta d_3=1$ and $theta d_1geq 0$, $theta d_2geq 0$ and $1+theta d_3geq 0$ for all $thetain (0,delta)$. Since $thetain (0,delta)$, this is equivalent to $$d_1+d_2+d_3=0,quad d_1,d_2geq 0,quad theta d_3geq -1$$ for all $thetain (0,delta)$. This defines the feasible directions.
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
edited Nov 26 '16 at 21:31
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
answered Nov 26 '16 at 10:27
AnonymousIGuessAnonymousIGuess
1519
1519
add a comment |
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$begingroup$
$x = (0,0,1)$ is a point on the boundary of $P$ (note that $0 + 0 + 1 = 1$). From the definition of feasible direction, in this case, it means a direction that points into $P$, instead of outside. Hint: this $P$ lines within a plane (and if I am correct in interpreting "$x ge 0$" to mean $x_1 ge 0, x_2 ge 0, x_3 ge 0$, then $P$ is a triangle in that plane, with $x$ as one of its vertices).
$endgroup$
– Paul Sinclair
Nov 27 '15 at 5:10