Solution to constrained quadratic optimization problem
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Is there a closed form solution to this constrained quadratic optimization problem?
$$
mathrm{argmax}_X mathrm{Tr}(AX)mathrm{Tr}(BX)\
0preceq Xpreceq I
$$
Where $A$ and $B$ are hermitian positive matrices and $Apreceq I$, $Bpreceq I$.
EDIT: The inequalities are with respect to the eigenvalues
convex-optimization
edited Nov 16 at 16:30
Brian Borchers
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
add a comment |
up vote
0
down vote
favorite
Is there a closed form solution to this constrained quadratic optimization problem?
$$
mathrm{argmax}_X mathrm{Tr}(AX)mathrm{Tr}(BX)\
0preceq Xpreceq I
$$
Where $A$ and $B$ are hermitian positive matrices and $Apreceq I$, $Bpreceq I$.
EDIT: The inequalities are with respect to the eigenvalues
convex-optimization
edited Nov 16 at 16:30
Brian Borchers
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
1
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there a closed form solution to this constrained quadratic optimization problem?
$$
mathrm{argmax}_X mathrm{Tr}(AX)mathrm{Tr}(BX)\
0preceq Xpreceq I
$$
Where $A$ and $B$ are hermitian positive matrices and $Apreceq I$, $Bpreceq I$.
EDIT: The inequalities are with respect to the eigenvalues
convex-optimization
edited Nov 16 at 16:30
Brian Borchers
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
Is there a closed form solution to this constrained quadratic optimization problem?
$$
mathrm{argmax}_X mathrm{Tr}(AX)mathrm{Tr}(BX)\
0preceq Xpreceq I
$$
Where $A$ and $B$ are hermitian positive matrices and $Apreceq I$, $Bpreceq I$.
EDIT: The inequalities are with respect to the eigenvalues
convex-optimization
convex-optimization
edited Nov 16 at 16:30
Brian Borchers
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
edited Nov 16 at 16:30
Brian Borchers
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
edited Nov 16 at 16:30
Brian Borchers
5,51611119
edited Nov 16 at 16:30
Brian Borchers
5,51611119
edited Nov 16 at 16:30
Brian Borchers
5,51611119
5,51611119
asked Nov 16 at 16:17
Ziofil
571416
asked Nov 16 at 16:17
Ziofil
571416
asked Nov 16 at 16:17
Ziofil
571416
571416
1
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28
add a comment |
1
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28
1
1
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28
add a comment |
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1
By $leq$, do you mean element wise inequality or conic inequality with respect to the semidefinite cone?
– Brian Borchers
Nov 16 at 16:23
Thank you for the question, see edit.
– Ziofil
Nov 16 at 16:25
The notation $succeq$ is normally used for this kind of conic inequality.
– Brian Borchers
Nov 16 at 16:26
Fixed. Thank you.
– Ziofil
Nov 16 at 16:28