Replacing square-root term in optimization constraint?
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I am implementing an optimization problem using semi-definite problem. One of my constraints is of following form
$$trace(A*X)- (k * trace(A*X))+ (k * sqrt{trace(B*X)})==0$$
where k is a constant, $A$ and $B$ are constant complex hermitian matrices and $X$ is $m*m$ complex, hermitian semi definite matrix optimization variable.
It can be seen that the last terms $sqrt{trace(B*X)}$ is a problematic term. Since, I am writing my code using YALMIP, which is an external toolbox of MATLAB, sqrt on complex variable is not allowed in that toolbox. Is there any way to rewrite that particular term using some convex optimization tools so that I can implement it easily in YALMIP?
convex-analysis convex-optimization
asked yesterday
Muhammad Usman
85
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I am implementing an optimization problem using semi-definite problem. One of my constraints is of following form
$$trace(A*X)- (k * trace(A*X))+ (k * sqrt{trace(B*X)})==0$$
where k is a constant, $A$ and $B$ are constant complex hermitian matrices and $X$ is $m*m$ complex, hermitian semi definite matrix optimization variable.
It can be seen that the last terms $sqrt{trace(B*X)}$ is a problematic term. Since, I am writing my code using YALMIP, which is an external toolbox of MATLAB, sqrt on complex variable is not allowed in that toolbox. Is there any way to rewrite that particular term using some convex optimization tools so that I can implement it easily in YALMIP?
convex-analysis convex-optimization
asked yesterday
Muhammad Usman
85
Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago
add a comment |
up vote
0
down vote
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up vote
0
down vote
favorite
I am implementing an optimization problem using semi-definite problem. One of my constraints is of following form
$$trace(A*X)- (k * trace(A*X))+ (k * sqrt{trace(B*X)})==0$$
where k is a constant, $A$ and $B$ are constant complex hermitian matrices and $X$ is $m*m$ complex, hermitian semi definite matrix optimization variable.
It can be seen that the last terms $sqrt{trace(B*X)}$ is a problematic term. Since, I am writing my code using YALMIP, which is an external toolbox of MATLAB, sqrt on complex variable is not allowed in that toolbox. Is there any way to rewrite that particular term using some convex optimization tools so that I can implement it easily in YALMIP?
convex-analysis convex-optimization
asked yesterday
Muhammad Usman
85
I am implementing an optimization problem using semi-definite problem. One of my constraints is of following form
$$trace(A*X)- (k * trace(A*X))+ (k * sqrt{trace(B*X)})==0$$
where k is a constant, $A$ and $B$ are constant complex hermitian matrices and $X$ is $m*m$ complex, hermitian semi definite matrix optimization variable.
It can be seen that the last terms $sqrt{trace(B*X)}$ is a problematic term. Since, I am writing my code using YALMIP, which is an external toolbox of MATLAB, sqrt on complex variable is not allowed in that toolbox. Is there any way to rewrite that particular term using some convex optimization tools so that I can implement it easily in YALMIP?
convex-analysis convex-optimization
convex-analysis convex-optimization
asked yesterday
Muhammad Usman
85
asked yesterday
Muhammad Usman
85
edited 23 hours ago
asked yesterday
Muhammad Usman
85
asked yesterday
Muhammad Usman
85
asked yesterday
Muhammad Usman
85
85
Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago
add a comment |
Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago
Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago
add a comment |
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Why do you think a nonlinear equality constraint is convex to begin with?
– LinAlg
20 hours ago
I didn't say that the posted equation is convex. If I remove the sqrt term from the equation, then the equation is becomes linear in terms of X and thus convex. That's the reason I am asking is there any mathematical way to rewrite the sqrt term such that my equation become linear again and the sqrt term is handled separately in such a way that I maintain the convexity of my problem.
– Muhammad Usman
19 hours ago