constraint equation

A fixed relationship tying a problem's variables together, used to eliminate one variable by substitution.

The constraint equation is the fixed relationship among an optimization problem's variables — a budget, a fixed amount of material, a fixed length of fencing. When it can be solved explicitly for one variable in terms of the other, substituting it into the objective function collapses the problem into a single-variable one; the geometry does the substitution's job before any algebra happens.

Examples

A box built from exactly $48\text{ ft}^2$ of material has constraint equation $x^2+4xh=48$ , solved as $h=\dfrac{48-x^2}{4x}$ .