# Feasible

A point is feasible if it satisfies all constraints. The feasible region (or feasibility region) is the set of all feasible points. A mathematical program is feasible if its feasible region is not empty.

The term feasible doesn't imbue other properties such as convexity or connectedness. For example, a feasible region to a nonlinear program could be $LaTeX: \{ x : x^2 \ge 1 \}$, which is the disjoint union $LaTeX: \{x : x \ge 1 \} \cap \{x : x \le -1\}$.

# Convex set

If any two points are in the set, so is their line segment, i.e.

$LaTeX: x, y \in X \Rightarrow (1 - a) x + a y \in X$,

for any $LaTeX: 0 \le a \le 1$. See Myths and Counter Examples in Mathematical Programming.