for at least one basic variable. During the next pivot, the minimum-ratio test may give a ratio of zero. This means the entering variable can enter the basis while the value of the objective function remains unchanged.

Yes, degeneracy can trap the Simplex algorithm in an infinite loop by cycling through the exact same corner point without improving the objective value. Anti-cycling rules, such as Bland's rule, prevent this by enforcing strict deterministic tie-breaking based on variable indices to guarantee that a repeating loop never occurs.

Yes, a computer running the Simplex algorithm can sometimes get stuck in an infinite loop, called cycling, when the problem has a degenerate solution. Anti-cycling rules, such as Bland’s Rule, ensure that the algorithm chooses variables in a consistent way to avoid returning to the same corner point. This guarantees that the Simplex method will eventually move toward an optimal solution or determine that none exists.

Degeneracy occurs when a basic variable evaluates to zero ($x_i = 0$). Geometrically, this means more constraint hyperplanes intersect at a single corner point than are necessary to define it in $n$-dimensional space (e.g., three lines intersecting at a single point on a 2D plane instead of two).

degeneracy can cause the Simplex algorithm to cycle endlessly through the same sequence of bases without improving the objective value, but anti-cycling strategies like Bland's rule prevent this by applying strict, deterministic tie-breaking criteria for selecting entering and leaving variables.

Yes, the Simplex algorithm can theoretically get trapped in an infinite loop, called cycling, where it repeatedly visits the same basic feasible solution due to degeneracy. Anti-cycling rules such as Bland’s Rule prevent this by using a consistent rule for choosing the entering and leaving variables, ensuring that the algorithm eventually moves to a different solution and terminates.

Degeneracy occurs when a basic variable equals zero, causing zero-step pivots that stall objective value progress and risk infinite cycling, which anti-cycling rules like Bland’s Smallest-Index Rule prevent.

Yes. In some degenerate cases, the Simplex method can cycle and revisit the same basic solution repeatedly. Anti-cycling rules, such as Bland’s Rule, prevent this by using a consistent rule for choosing the entering and leaving variables, ensuring that the algorithm eventually moves toward an optimal solution.