specific assignments of vector items

I am looking for suitable algorithm to solve the following problem:

For vector v (Nx1, double, single) I need to find assigments of items of this vector (pairs) that fulfil following conditions:

1. Each item is in assigned in only one pair
2. sum of item distances over all assigned pairs (violation) is minimal
3. as an input of the function is additional parameter vio_max which limits violation of non assignment

[pairs,dist, vio] = findpairs(v,vio_max)

ExampleA:

Input: v = [3.0 2.1 0.9 2.9 1.1 ] , vio_max = 1.0

Output: pairs = [1 4; 3 5], dist = [0.1; 0.2], vio = sum(dist) = 0.3

and item 2.1 remains unassigned (for lenght(v) is odd)

ExampleB:

Input: v = [3.0 2.1 0.9 2.9 1.1 ] , vio_max = 0.15

Output: pairs = [1 4], dist = [0.1], vio = sum(dist) = 0.1