Convexity of the Feasible Region in Linear Programming
Students often conflate 'convexity' with 'compactness'. A feasible region can be convex but unbounded (e.g., in a minimization problem with an open constraint set). Convexity guarantees that no 'local' traps exist, but it does not guarantee that a finite optimal solution exists without further bounds.
Institutional Reference: Fundamentals of Optimization
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