Formula for volume of a convex polytopeAlgorithm for finding the volume of a convex polytopeAlgorithm for finding the volume of a convex polytopeDo plane projections determine a convex polytope?Estimating the Volume of the Metric PolytopeRandom Sampling a linearly constrained region in n-dimensions…Complexity of convex polytope volume calculation ? (Volume of Voronoi cell) (Error probability)Volume of intersection of a convex polytope with an affine space.non-convex Polytope definitionconvex polytope integer pointsEfficient algorithm for finding normals of a high dimensional convex hull with few facetsVolume of caps of a polytope
Formula for volume of a convex polytope
Algorithm for finding the volume of a convex polytopeAlgorithm for finding the volume of a convex polytopeDo plane projections determine a convex polytope?Estimating the Volume of the Metric PolytopeRandom Sampling a linearly constrained region in n-dimensions…Complexity of convex polytope volume calculation ? (Volume of Voronoi cell) (Error probability)Volume of intersection of a convex polytope with an affine space.non-convex Polytope definitionconvex polytope integer pointsEfficient algorithm for finding normals of a high dimensional convex hull with few facetsVolume of caps of a polytope
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So I've been searching around the internet for some answers to this, but I currently have a set of linear constraints: $Ax = b, Cx le d$ for matrices $A in mathbbR^n times m$, $bin mathbbR^n$, $C in mathbbR^p times m$, and $d in mathbbR^p$. I would like to deduce a formula for the volume of the set of feasible $x$:s that satisfy these constraints. It would be great if anyone could point me in a good direction, maybe this can't be solved analytically, in this case, maybe there is an approximation?
convex-polytopes linear-programming simplicial-volume
asked 10 hours ago
ErikErik
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So I've been searching around the internet for some answers to this, but I currently have a set of linear constraints: $Ax = b, Cx le d$ for matrices $A in mathbbR^n times m$, $bin mathbbR^n$, $C in mathbbR^p times m$, and $d in mathbbR^p$. I would like to deduce a formula for the volume of the set of feasible $x$:s that satisfy these constraints. It would be great if anyone could point me in a good direction, maybe this can't be solved analytically, in this case, maybe there is an approximation?
convex-polytopes linear-programming simplicial-volume
asked 10 hours ago
ErikErik
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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So I've been searching around the internet for some answers to this, but I currently have a set of linear constraints: $Ax = b, Cx le d$ for matrices $A in mathbbR^n times m$, $bin mathbbR^n$, $C in mathbbR^p times m$, and $d in mathbbR^p$. I would like to deduce a formula for the volume of the set of feasible $x$:s that satisfy these constraints. It would be great if anyone could point me in a good direction, maybe this can't be solved analytically, in this case, maybe there is an approximation?
convex-polytopes linear-programming simplicial-volume
asked 10 hours ago
ErikErik
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
So I've been searching around the internet for some answers to this, but I currently have a set of linear constraints: $Ax = b, Cx le d$ for matrices $A in mathbbR^n times m$, $bin mathbbR^n$, $C in mathbbR^p times m$, and $d in mathbbR^p$. I would like to deduce a formula for the volume of the set of feasible $x$:s that satisfy these constraints. It would be great if anyone could point me in a good direction, maybe this can't be solved analytically, in this case, maybe there is an approximation?
convex-polytopes linear-programming simplicial-volume
convex-polytopes linear-programming simplicial-volume
asked 10 hours ago
ErikErik
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
ErikErik
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 9 hours ago
Erik
asked 10 hours ago
ErikErik
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 10 hours ago
ErikErik
212
asked 10 hours ago
ErikErik
212
212
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Erik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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Check out our Code of Conduct.
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Here is one paper, whose introduction will lead you to others:
Lasserre, Jean B., and Eduardo S. Zeron. "A new algorithm for the volume of a convex polytope." arXiv math/0106168 (2001).
If you want a faster but approximate algorithm:
Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient random-walk methods for approximating polytope volume." In Proceedings 13th Symposium on Computational Geometry, p. 318. ACM, 2014. ACM link.
Also addressed in a 2009 MO question:
"Algorithm for finding the volume of a convex polytope."
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
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1 Answer
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1 Answer
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active
oldest
votes
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active
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$begingroup$
Here is one paper, whose introduction will lead you to others:
Lasserre, Jean B., and Eduardo S. Zeron. "A new algorithm for the volume of a convex polytope." arXiv math/0106168 (2001).
If you want a faster but approximate algorithm:
Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient random-walk methods for approximating polytope volume." In Proceedings 13th Symposium on Computational Geometry, p. 318. ACM, 2014. ACM link.
Also addressed in a 2009 MO question:
"Algorithm for finding the volume of a convex polytope."
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
$endgroup$
add a comment |
$begingroup$
Here is one paper, whose introduction will lead you to others:
Lasserre, Jean B., and Eduardo S. Zeron. "A new algorithm for the volume of a convex polytope." arXiv math/0106168 (2001).
If you want a faster but approximate algorithm:
Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient random-walk methods for approximating polytope volume." In Proceedings 13th Symposium on Computational Geometry, p. 318. ACM, 2014. ACM link.
Also addressed in a 2009 MO question:
"Algorithm for finding the volume of a convex polytope."
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
$endgroup$
add a comment |
$begingroup$
Here is one paper, whose introduction will lead you to others:
Lasserre, Jean B., and Eduardo S. Zeron. "A new algorithm for the volume of a convex polytope." arXiv math/0106168 (2001).
If you want a faster but approximate algorithm:
Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient random-walk methods for approximating polytope volume." In Proceedings 13th Symposium on Computational Geometry, p. 318. ACM, 2014. ACM link.
Also addressed in a 2009 MO question:
"Algorithm for finding the volume of a convex polytope."
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
$endgroup$
Here is one paper, whose introduction will lead you to others:
Lasserre, Jean B., and Eduardo S. Zeron. "A new algorithm for the volume of a convex polytope." arXiv math/0106168 (2001).
If you want a faster but approximate algorithm:
Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient random-walk methods for approximating polytope volume." In Proceedings 13th Symposium on Computational Geometry, p. 318. ACM, 2014. ACM link.
Also addressed in a 2009 MO question:
"Algorithm for finding the volume of a convex polytope."
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
edited 7 hours ago
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
85.7k16234703
85.7k16234703
add a comment |
add a comment |
Erik is a new contributor. Be nice, and check out our Code of Conduct.
Erik is a new contributor. Be nice, and check out our Code of Conduct.
Erik is a new contributor. Be nice, and check out our Code of Conduct.
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