Constraint vs. Restriction

You may find the entries within websters-dictionary-online.net's “Specialty Definition” sections for these words useful. For example, two of the several entries there include:

[Noun] Limitation; confinement within bounds. This is to have the same restriction as all other recreations. Restriction of words is the limitation of their signification in a particular manner or degree. Source: Webster's 1828 American Dictionary. [Specialty Definition: restriction]

[Noun] Irresistible force, or its effect; any force, or power, physical or moral, which compels to act or to forbear action, or which urges so strongly as to produce its effect upon the body or mind; compulsion; restraint; confinement. Not by constraint, but by my choice, I came. Feed the flock of God, taking the oversight thereof, not by constraint, but willingly. 1 Peter 5.. Source: Webster's 1828 American Dictionary. [Specialty Definition: constraint]

I generally think of constraints as restrictions that are intrinsic to a problem or situation (thus, more of an ab initio nature than ex post facto) and of restrictions as constraints that are imposed upon a problem or situation (thus, more of an ex post facto nature than ab initio). That is, I think Bill Franke has it backwards.

For example, an ordinary linear-programming problem is subject to hyperplane constraints; for example, the amount of X in some product, plus the amount of Y, not to exceed some limit Z. If on top of such constraints it were dictated that solutions must have integer values, one would speak of restricting the solution, rather than constraining it.

Constraints affects decision variables interaction, i.e x+y+z<=A.

Restrictions limits the value for each variable, i.e. x,y,z >=0

Regards