I need to minimize the L2,1 norm of a matrix,that is ||X||_{2,1}=\sum_i(\sum_j x_{ij}^2)^{\frac{1}{2}},

I tried many methods to no avail, but finally found a method, but this method only worked in the beginning and not in subsequent iterations.

If X is a 100 by 8 matrix，Then the way I implement L2,1 norm is like this

minimize( norm(X(1,:),2)+norm(X(2,:),2)+norm(X(3,:),2)+norm(X(4,:),2)+norm(X(5,:),2) …

+norm(X(6,:),2)+norm(X(7,:),2)+norm(X(8,:),2)+norm(X(9,:),2)+norm(X(10,:),2) …

+norm(X(11,:),2)+norm(X(12,:),2)+norm(X(13,:),2)+norm(X(14,:),2)+norm(X(15,:),2) …

+norm(X(16,:),2)+norm(X(17,:),2)+norm(X(18,:),2)+norm(X(19,:),2)+norm(X(20,:),2) …

+norm(X(21,:),2)+norm(X(22,:),2)+norm(X(23,:),2)+norm(X(24,:),2)+norm(X(25,:),2) …

+norm(X(26,:),2)+norm(X(27,:),2)+norm(X(28,:),2)+norm(X(29,:),2)+norm(X(30,:),2) …

+norm(X(31,:),2)+norm(X(32,:),2)+norm(X(33,:),2)+norm(X(34,:),2)+norm(X(35,:),2) …

+norm(X(36,:),2)+norm(X(37,:),2)+norm(X(38,:),2)+norm(X(39,:),2)+norm(X(40,:),2) …

+norm(X(41,:),2)+norm(X(42,:),2)+norm(X(43,:),2)+norm(X(44,:),2)+norm(X(45,:),2) …

+norm(X(46,:),2)+norm(X(47,:),2)+norm(X(48,:),2)+norm(X(49,:),2)+norm(X(50,:),2) …

+norm(X(51,:),2)+norm(X(52,:),2)+norm(X(53,:),2)+norm(X(54,:),2)+norm(X(55,:),2) …

+norm(X(56,:),2)+norm(X(57,:),2)+norm(X(58,:),2)+norm(X(59,:),2)+norm(X(60,:),2) …

+norm(X(61,:),2)+norm(X(62,:),2)+norm(X(63,:),2)+norm(X(64,:),2)+norm(X(65,:),2) …

+norm(X(66,:),2)+norm(X(67,:),2)+norm(X(68,:),2)+norm(X(69,:),2)+norm(X(70,:),2) …

+norm(X(71,:),2)+norm(X(72,:),2)+norm(X(73,:),2)+norm(X(74,:),2)+norm(X(75,:),2) …

+norm(X(76,:),2)+norm(X(77,:),2)+norm(X(78,:),2)+norm(X(79,:),2)+norm(X(80,:),2) …

+norm(X(81,:),2)+norm(X(82,:),2)+norm(X(83,:),2)+norm(X(84,:),2)+norm(X(85,:),2) …

+norm(X(86,:),2)+norm(X(87,:),2)+norm(X(88,:),2)+norm(X(89,:),2)+norm(X(90,:),2) …

+norm(X(91,:),2)+norm(X(92,:),2)+norm(X(93,:),2)+norm(X(94,:),2)+norm(X(95,:),2) …

+norm(X(96,:),2)+norm(X(97,:),2)+norm(X(98,:),2)+norm(X(99,:),2)+norm(X(100,:),2) …

);

Although this is very cumbersome, it can still be achieved.

This method is only suitable for initializing X_0，After that I will take certain rows from X to minimize, this step is what confuses me the most,If it cannot be made to automatically loop, I will have to manually find the support set T_l at each step and manually modify the expression of minimize。

Then I thought of a way。

expression Z(n);

for i =1:n

Z(i)=norm(X(i,:),2);

end

but the answer is different when you minimize（Z（1）） and minimize(norm(X(1,:),2))

This makes me unable to proceed, so I would like to know if there is any way to achieve it.