In optimization, strict inequalities do not make sense. What is the solution to the model

min x, subject to x > 0 ? Is it 1.e-10 or 1.e-20 or something smaller.

Optimization theory is usually concerned with bounded closed sets where closed means that the boundary is part of the feasible set. Thus there is no difference between < and < = for continuous variables when dealing with numerical algorithms. For discrete variables, the constraints mean exactly what they say. =L= means < =, thus a constraint with an integer variable =L= 9 means it can be less or equal to 9. If you want it to be less than 9, write the constraint as =L= 8.