Minimizing mixed-norm subject to a nonconvex quartic constraint for small n and m












0














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







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  • 1




    This is not a convex problem, so you should remove that tag
    – Johan Löfberg
    17 hours ago






  • 2




    ...and it is not a quadratic constraint, it is quartic
    – Johan Löfberg
    17 hours ago










  • Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
    – kogito
    16 hours ago






  • 1




    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.
    – Johan Löfberg
    13 hours ago
















0














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







share|cite|improve this question









New contributor




kogito is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    This is not a convex problem, so you should remove that tag
    – Johan Löfberg
    17 hours ago






  • 2




    ...and it is not a quadratic constraint, it is quartic
    – Johan Löfberg
    17 hours ago










  • Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
    – kogito
    16 hours ago






  • 1




    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.
    – Johan Löfberg
    13 hours ago














0












0








0







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







share|cite|improve this question









New contributor




kogito is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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






share|cite|improve this question









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kogito is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









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Check out our Code of Conduct.









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edited 13 hours ago





















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asked 19 hours ago









kogito

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kogito is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






kogito is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    This is not a convex problem, so you should remove that tag
    – Johan Löfberg
    17 hours ago






  • 2




    ...and it is not a quadratic constraint, it is quartic
    – Johan Löfberg
    17 hours ago










  • Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
    – kogito
    16 hours ago






  • 1




    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.
    – Johan Löfberg
    13 hours ago














  • 1




    This is not a convex problem, so you should remove that tag
    – Johan Löfberg
    17 hours ago






  • 2




    ...and it is not a quadratic constraint, it is quartic
    – Johan Löfberg
    17 hours ago










  • Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
    – kogito
    16 hours ago






  • 1




    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.
    – Johan Löfberg
    13 hours ago








1




1




This is not a convex problem, so you should remove that tag
– Johan Löfberg
17 hours ago




This is not a convex problem, so you should remove that tag
– Johan Löfberg
17 hours ago




2




2




...and it is not a quadratic constraint, it is quartic
– Johan Löfberg
17 hours ago




...and it is not a quadratic constraint, it is quartic
– Johan Löfberg
17 hours ago












Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
– kogito
16 hours ago




Thank you for your comment. The problem is taken from this paper and there they mention that it is quadratic.
– kogito
16 hours ago




1




1




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.
– Johan Löfberg
13 hours ago




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.
– Johan Löfberg
13 hours ago










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