Minimizing mixed-norm subject to a nonconvex quartic constraint for small n and m
0
$begingroup$
How can one solve this mixed-norm minimization problem subject to a quartic constraint for small N and M (ex: M=12 and N=4):
- $textbf{c} = [c_{1},...,c_{N}]^T$
- $minbiggl (|textbf{c}|_{1} + beta|textbf{c}|_{2} ^2biggr) subjectspace
tospace sumlimits_ {m=1} ^M (|v_ {m} |^2-textbf{c}^Htextbf{a}_mtextbf{a}_m^Htextbf{c})
^2leqepsilon$
Thank you for advance for any suggestions.
optimization qcqp
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
$endgroup$
add a comment |
0
$begingroup$
How can one solve this mixed-norm minimization problem subject to a quartic constraint for small N and M (ex: M=12 and N=4):
- $textbf{c} = [c_{1},...,c_{N}]^T$
- $minbiggl (|textbf{c}|_{1} + beta|textbf{c}|_{2} ^2biggr) subjectspace
tospace sumlimits_ {m=1} ^M (|v_ {m} |^2-textbf{c}^Htextbf{a}_mtextbf{a}_m^Htextbf{c})
^2leqepsilon$
Thank you for advance for any suggestions.
optimization qcqp
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
$endgroup$
1
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
2
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
1
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07
add a comment |
0
0
0
$begingroup$
How can one solve this mixed-norm minimization problem subject to a quartic constraint for small N and M (ex: M=12 and N=4):
- $textbf{c} = [c_{1},...,c_{N}]^T$
- $minbiggl (|textbf{c}|_{1} + beta|textbf{c}|_{2} ^2biggr) subjectspace
tospace sumlimits_ {m=1} ^M (|v_ {m} |^2-textbf{c}^Htextbf{a}_mtextbf{a}_m^Htextbf{c})
^2leqepsilon$
Thank you for advance for any suggestions.
optimization qcqp
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
$endgroup$
How can one solve this mixed-norm minimization problem subject to a quartic constraint for small N and M (ex: M=12 and N=4):
- $textbf{c} = [c_{1},...,c_{N}]^T$
- $minbiggl (|textbf{c}|_{1} + beta|textbf{c}|_{2} ^2biggr) subjectspace
tospace sumlimits_ {m=1} ^M (|v_ {m} |^2-textbf{c}^Htextbf{a}_mtextbf{a}_m^Htextbf{c})
^2leqepsilon$
Thank you for advance for any suggestions.
optimization qcqp
optimization qcqp
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
edited Jan 4 at 21:35
SuperKogito
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
asked Jan 4 at 14:58
SuperKogitoSuperKogito
1035
1035
1
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
2
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
1
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07
add a comment |
1
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
2
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
1
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07
1
1
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
2
2
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
1
1
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07
add a comment |
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1
$begingroup$
This is not a convex problem, so you should remove that tag
$endgroup$
– Johan Löfberg
Jan 4 at 17:21
2
$begingroup$
...and it is not a quadratic constraint, it is quartic
$endgroup$
– Johan Löfberg
Jan 4 at 17:22
$begingroup$
Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
$endgroup$
– SuperKogito
Jan 4 at 17:50
1
$begingroup$
Well that is obviously incorrect as you have a square of a quadratic. What they do is that they write the nonconvex quartic model as a rank-constrained (thus non-convex) semidefinite program with a convex quadratic constraint.
$endgroup$
– Johan Löfberg
Jan 4 at 21:07