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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 setbutton.png

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.

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