Help with matrix selection in matlab
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I have this equalities, with $Delta X$ and $Delta S$ unknown matrices, $X$, $S$ and $tau$ known. $$W^{-1}Delta X W^{-1}+Delta S=tau X^{-1}-S$$or equivalently $$Delta X + WDelta S W=tau S^{-1}-X$$
My first question is how can i compute, or how can i find $Delta X$.
My second question is, that given the following sets: $$N_mathcal{F}(theta):={(X,y,S)inmathcal{F}^0 : d_mathcal{F}(X,S)leqthetamu(X,S)}$$
and $$mathcal{F}^0:={(X,y,S):textbf{tr}(A_iX)=b_i; sum_{i=1}^my_iA_i+S=C; X,Ssucc 0;, i=1,...,m}$$
Wher $theta, C, A_i$ are given, and $$d_mathcal{F}(X,S)=||S^{1/}2XS^{1/2}-mu(X,S)I||_F$$ $$mu(X,S)=textbf{tr}(XS)/n$$
With $n=size(X)$.
How can i find, or compute in matlab, a fesasible pair $(X^0,S^0)in N_mathcal{F}(theta)$
matrices optimization convex-optimization matlab positive-semidefinite
asked Nov 13 at 17:09
Vicente Merino
213
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up vote
0
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I have this equalities, with $Delta X$ and $Delta S$ unknown matrices, $X$, $S$ and $tau$ known. $$W^{-1}Delta X W^{-1}+Delta S=tau X^{-1}-S$$or equivalently $$Delta X + WDelta S W=tau S^{-1}-X$$
My first question is how can i compute, or how can i find $Delta X$.
My second question is, that given the following sets: $$N_mathcal{F}(theta):={(X,y,S)inmathcal{F}^0 : d_mathcal{F}(X,S)leqthetamu(X,S)}$$
and $$mathcal{F}^0:={(X,y,S):textbf{tr}(A_iX)=b_i; sum_{i=1}^my_iA_i+S=C; X,Ssucc 0;, i=1,...,m}$$
Wher $theta, C, A_i$ are given, and $$d_mathcal{F}(X,S)=||S^{1/}2XS^{1/2}-mu(X,S)I||_F$$ $$mu(X,S)=textbf{tr}(XS)/n$$
With $n=size(X)$.
How can i find, or compute in matlab, a fesasible pair $(X^0,S^0)in N_mathcal{F}(theta)$
matrices optimization convex-optimization matlab positive-semidefinite
asked Nov 13 at 17:09
Vicente Merino
213
Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have this equalities, with $Delta X$ and $Delta S$ unknown matrices, $X$, $S$ and $tau$ known. $$W^{-1}Delta X W^{-1}+Delta S=tau X^{-1}-S$$or equivalently $$Delta X + WDelta S W=tau S^{-1}-X$$
My first question is how can i compute, or how can i find $Delta X$.
My second question is, that given the following sets: $$N_mathcal{F}(theta):={(X,y,S)inmathcal{F}^0 : d_mathcal{F}(X,S)leqthetamu(X,S)}$$
and $$mathcal{F}^0:={(X,y,S):textbf{tr}(A_iX)=b_i; sum_{i=1}^my_iA_i+S=C; X,Ssucc 0;, i=1,...,m}$$
Wher $theta, C, A_i$ are given, and $$d_mathcal{F}(X,S)=||S^{1/}2XS^{1/2}-mu(X,S)I||_F$$ $$mu(X,S)=textbf{tr}(XS)/n$$
With $n=size(X)$.
How can i find, or compute in matlab, a fesasible pair $(X^0,S^0)in N_mathcal{F}(theta)$
matrices optimization convex-optimization matlab positive-semidefinite
asked Nov 13 at 17:09
Vicente Merino
213
I have this equalities, with $Delta X$ and $Delta S$ unknown matrices, $X$, $S$ and $tau$ known. $$W^{-1}Delta X W^{-1}+Delta S=tau X^{-1}-S$$or equivalently $$Delta X + WDelta S W=tau S^{-1}-X$$
My first question is how can i compute, or how can i find $Delta X$.
My second question is, that given the following sets: $$N_mathcal{F}(theta):={(X,y,S)inmathcal{F}^0 : d_mathcal{F}(X,S)leqthetamu(X,S)}$$
and $$mathcal{F}^0:={(X,y,S):textbf{tr}(A_iX)=b_i; sum_{i=1}^my_iA_i+S=C; X,Ssucc 0;, i=1,...,m}$$
Wher $theta, C, A_i$ are given, and $$d_mathcal{F}(X,S)=||S^{1/}2XS^{1/2}-mu(X,S)I||_F$$ $$mu(X,S)=textbf{tr}(XS)/n$$
With $n=size(X)$.
How can i find, or compute in matlab, a fesasible pair $(X^0,S^0)in N_mathcal{F}(theta)$
matrices optimization convex-optimization matlab positive-semidefinite
matrices optimization convex-optimization matlab positive-semidefinite
asked Nov 13 at 17:09
Vicente Merino
213
asked Nov 13 at 17:09
Vicente Merino
213
asked Nov 13 at 17:09
Vicente Merino
213
asked Nov 13 at 17:09
Vicente Merino
213
asked Nov 13 at 17:09
Vicente Merino
213
213
Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12
add a comment |
Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12
Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12
add a comment |
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Its better to split these questions into two threads. Regarding your first question, it is not obvious that these equations are equivalent, please clarify.
– The Pheromone Kid
Nov 13 at 18:02
I agree with @Adrian Schad : there is first a question of equivalence ; besides, we don't know the status of $Delta S$. If it is known, we would have plainly $$Delta X = -WDelta S W+tau S^{-1}-X...$$ Otherwise you are looking for an unknown pair $(Delta X,Delta S)$. Is that the right interpretation ?
– Jean Marie
Nov 15 at 10:12