Hello. I cannot understand what 'RELAX' means in the following statement. Standard neoclassical modeling assumptions are then RELAXED. Assumptions are relaxed? Does that mean assumptions get useless?

No, it means the rules are relaxed or loosened. In whatever situation you are describing, the assumptions are no longer as strictly applied.
I cannot understand what 'RELAX' means in the following statement. "Standard neoclassical modeling assumptions are then RELAXED."

It means assumptions are broadened or, when taken to the extreme, eliminated.
A model is a simplified representation of something in the real world. In order to generate such a simplified representation, assumptions are made about the true nature of that something.

For example, one can model the three-dimensional structure of DNA based upon the assumption that the axial length of an A:T hydrogen- bonded base pair is the same as that of a G:C base pair. The value of this assumption is that it makes constructing the model simpler.

However, in reality, A:T and G:C base pairs have slightly different lengths. By relaxing the assumption that they have the same length, one constructs a model that is a more accurate representation of reality, but at the expense of greater difficulty in its construction.
Once this particular assumption is relaxed, additional assumptions must be made. For example, one could assume that the length of a base pair does not depend on the identity of its neighboring base pairs. Or one could relax this assumption and assume that the length of a base pair depends on the identity of the nearest base pairs on either side. One could relax this assumption even further by assuming that the length of a base pair depends upon the identity of the two nearest base pairs on either side. When this assumption about neighbor-dependence is relaxed completely, one assumes that the length of a base pair depends upon the identity of every base pair in the entire DNA strand.
As a simpler example, consider a model of the geometric structure of the human face. One could assume that human faces are bilaterally mirror symmetric, and create a model in which the right and left sides are mirror images of one another. This model has the virtue that one only needs to generate a representation of a single side of the face, and then flip it over to render the representation of the other.
Or one could relax this assumption and allow the right and left sides to vary from exact symmetry. This second model is more accurate, but at the expense of greater difficulty in its construction; now one needs to generate separate representations of the two sides of the face.

Mike Nitabach
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I cannot understand what 'RELAX' means in the following statement. Standard neoclassical modeling assumptions are then RELAXED. Assumptions are relaxed? Does that mean assumptions get useless?

From (COD11)
relax
· v.

3 make (a rule or restriction) less strict.