When you arrayfun() with matrices, the calculation is done with one element from each input matrix, so scalars are going to be passed into the function. You cannot then index the scalars.
If you want c to be a vector of length 100, then you need to pass a vector of length 100 in the position where you have passed 100. The first parameter to fminsearch is a function handle; the second parameter is the starting point vector, not the length of the starting point vector.
It appears to me you are trying to index a column of phi at a time. If so then what you should be passing to arrayfun is the vector of column numbers. Perhaps something like
c0 = ones(1,100);
c_hat = arrayfun(@(colidx) fminsearch(@(c) 1/2*(y(1:2,colidx).'*y(1:2,colidx)-(phi(:,colidx)*c)*(y(1:2,colidx)*c))+lambda*sum(c), c0, options), 1:size(phi,2), 'uniform', 0 );
You should re-check what I have written carefully as I might not have the right row vs column mix in the multiplications; I am pretty sure I got it wrong in places, because I am not certain what your calculation is trying to do.
