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Comparing Problem 1 and 2 determine which problem produce sparsest solution for W?
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Problem1:
min $|W^l2 |_1$
s.t $|A^K_i w_i - b^K_i|_2 leq varepsilon, text for i=1,2, ldots, gamma$
$;|A^L_i w_i| leq rho times 1^L$
where $A^K_i in mathbbC^K times N$, $A^L_i in mathbbC^L times N$, $W in mathbbC^Ntimes gamma$ and $W = [w_1 w_2 ldots w_gamma]$ and $K+L=M$.
Problem2:
min $ |AW-B|_F + lambda |W^l2|_1$
where $A in mathbbC^M times N$, $B in mathbbC^M times gamma$ and $lambda$ is the regularization parameter.
Thank you in advance.
convex-optimization sparsity
edited Jul 20 at 17:36
Michael Hardy
204k23186462
asked Jul 20 at 15:58
Arun Goel
11
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Problem1:
min $|W^l2 |_1$
s.t $|A^K_i w_i - b^K_i|_2 leq varepsilon, text for i=1,2, ldots, gamma$
$;|A^L_i w_i| leq rho times 1^L$
where $A^K_i in mathbbC^K times N$, $A^L_i in mathbbC^L times N$, $W in mathbbC^Ntimes gamma$ and $W = [w_1 w_2 ldots w_gamma]$ and $K+L=M$.
Problem2:
min $ |AW-B|_F + lambda |W^l2|_1$
where $A in mathbbC^M times N$, $B in mathbbC^M times gamma$ and $lambda$ is the regularization parameter.
Thank you in advance.
convex-optimization sparsity
edited Jul 20 at 17:36
Michael Hardy
204k23186462
asked Jul 20 at 15:58
Arun Goel
11
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Problem1:
min $|W^l2 |_1$
s.t $|A^K_i w_i - b^K_i|_2 leq varepsilon, text for i=1,2, ldots, gamma$
$;|A^L_i w_i| leq rho times 1^L$
where $A^K_i in mathbbC^K times N$, $A^L_i in mathbbC^L times N$, $W in mathbbC^Ntimes gamma$ and $W = [w_1 w_2 ldots w_gamma]$ and $K+L=M$.
Problem2:
min $ |AW-B|_F + lambda |W^l2|_1$
where $A in mathbbC^M times N$, $B in mathbbC^M times gamma$ and $lambda$ is the regularization parameter.
Thank you in advance.
convex-optimization sparsity
edited Jul 20 at 17:36
Michael Hardy
204k23186462
asked Jul 20 at 15:58
Arun Goel
11
Problem1:
min $|W^l2 |_1$
s.t $|A^K_i w_i - b^K_i|_2 leq varepsilon, text for i=1,2, ldots, gamma$
$;|A^L_i w_i| leq rho times 1^L$
where $A^K_i in mathbbC^K times N$, $A^L_i in mathbbC^L times N$, $W in mathbbC^Ntimes gamma$ and $W = [w_1 w_2 ldots w_gamma]$ and $K+L=M$.
Problem2:
min $ |AW-B|_F + lambda |W^l2|_1$
where $A in mathbbC^M times N$, $B in mathbbC^M times gamma$ and $lambda$ is the regularization parameter.
Thank you in advance.
convex-optimization sparsity
edited Jul 20 at 17:36
Michael Hardy
204k23186462
asked Jul 20 at 15:58
Arun Goel
11
edited Jul 20 at 17:36
Michael Hardy
204k23186462
edited Jul 20 at 17:36
Michael Hardy
204k23186462
edited Jul 20 at 17:36
Michael Hardy
204k23186462
204k23186462
asked Jul 20 at 15:58
Arun Goel
11
asked Jul 20 at 15:58
Arun Goel
11
asked Jul 20 at 15:58
Arun Goel
11
11
add a comment |Â
add a comment |Â
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