How to make sqrt(square(x)+square(a)) feasible?

1

Here’s my codes which are equation limits.
Where UAV_vertical_trajectory is variable and hor_distance0 is a known matrix.
distance = cvx( zeros(n,m) );
for i = 1:n
for j = 1:m
distance( i,j ) = sqrt( square(hor_distance0( i,j)) + square(UAV_vertical_trajectory( 1,j )) );
end
end
And the result I get is :Disciplined convex programming error:
Illegal operation: sqrt( {convex} ).

I hope to get the help of you.Thanks.

2

I would think you would have to do

|| linear expression || <= linear expression

You cannot have nonlinear equalities in a convex model.

3

Use
norm([x a])
in place of sqrt(square(x)+square(a))

You may be able to use norrms in place of for loop(s), by taking norms across all rows or all columns at once.

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.