Hi,

I want to my objective to be:

`objective<-Minimize(norm2(a-b[1,]) + norm2(a-b[2,]) + ..... + norm2(a-b[n,]))`

where

a=Variable(2)

b is n x 2 matrix

How can I define this objective?

Hi,

I want to my objective to be:

`objective<-Minimize(norm2(a-b[1,]) + norm2(a-b[2,]) + ..... + norm2(a-b[n,]))`

where

a=Variable(2)

b is n x 2 matrix

How can I define this objective?

You can use for loops to build up an objective. Or you can use `sum`

. In this case you can use `sum`

with `norms`

to get an efficient vectorized calculation.

```
cvx_begin
variable a(1,2)
minimize(sum(norms(repmat(a,n,1) - b,2,2)))
cvx_end
```

I leave you to check that this is correct. You can add constraints as appropriate.

help norms

norms Computation of multiple vector norms.

norms( X ) provides a means to compute the norms of multiple vectors

packed into a matrix or N-D array. This is useful for performing

max-of-norms or sum-of-norms calculations.`All of the vector norms, including the false "-inf" norm, supported by NORM() have been implemented in the norms() command. norms(X,P) = sum(abs(X).^P).^(1/P) norms(X) = norms(X,2). norms(X,inf) = max(abs(X)). norms(X,-inf) = min(abs(X)). If X is a vector, these computations are completely identical to their NORM equivalents. If X is a matrix, a row vector is returned of the norms of each column of X. If X is an N-D matrix, the norms are computed along the first non-singleton dimension. norms( X, [], DIM ) or norms( X, 2, DIM ) computes Euclidean norms along the dimension DIM. norms( X, P, DIM ) computes its norms along the dimension DIM. Disciplined convex programming information: norms is convex, except when P<1, so an error will result if these non-convex "norms" are used within CVX expressions. norms is nonmonotonic, so its input must be affine.`