A boundary case occurs when a parameter iterates to the "boundary" of the permissible "parameter space" (see Structural Equation Modeling). For example, a variance can only take on values from 0 to infinity. If, during iteration, the program attempts to move an estimate of a variance below zero, the program will constrain it to be on the boundary value of 0.

For some problems (for example a Heywood Case in factor analysis), it may be possible to reduce the discrepancy function by estimating a variance to be a negative number. In that case, the program does "the best it can" within the permissible parameter space, but does not actually obtain the "global minimum" of the discrepancy function.