I wanna to find individual values to minimize an outcome in a restriction.

*variables
- fac1, ..., fac15, persion1, con_month

*solutions which I want to get
- `a1', ... , `a15'

*minimize
- absolute value of [fac1*`a1' + ... + fac15*`a15' - pension1]

*restriction
-`a1' + ... + `a15' = con_month

*in each individual

I think that this problem may have multiple solutions and cannot lead to a proper solution.
Very thank you for your notice.