Introduction Let’s take a simple constrained problem (from Nocedal and Wright).
\begin{align*} \min \quad & x_1 + x_2\\ \textrm{s.t.} \quad & x_1^2 + x_2^2 - 2 = 0 \end{align*}
The set of possible solutions to this problem lie on the boundary of the circle defined by the constraint:
Figure 1: Source: Nocedal and Wright