Use `norm`

.

`S_1 = norm([L_r(1,1)-Q(1,1);L_r(1,2)-Q(1,2)])`

If you want to get fancier, you can use `norms`

with a matrix argument, and calculate all the S_i 's at once, placed into a vector.

help cvx/norm

Disciplined convex programming information:

norm is convex, except when P<1, so an error will result if

these non-convex “norms” are used within CVX expressions. norm

is nonmonotonic, so its input must be affine.

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.`

Thanks for your help！

I want to express the distance S_1<S_2, and S_1<3, but the problem of {convex} <= {convex} arises.

Those are non-convex constraints.

How to convert this non-convex constraint into a convex constraint

Have you read the link?

Non-convex optimization solvers (available under YALMIP, but not under CVX) exist because some optimization problems are non-convex.

Do you mean to use YALMIP this to solve this optimization problem? Do I need to put all my problems in YALMIP to use it?

If those are the constraints you need, then you can try YALMIP (you will need to use `sqrtm`

instead of `norm`

for the non-convex usage).

ok， thanks for your suggestion