Operations research
Guess first
Can the Simplex Method Loop Forever?
Most students think simplex always finishes. Guess first.
Quick check · tap an answer to continue
Lesson notes
Key points
- When a basic variable equals zero, a pivot can change the basis without improving the objective, which is called degeneracy.
- Such pivots can revisit the same bases forever, called cycling, but Bland's rule guarantees the method stops.
Definitions
- Degeneracy
- A basic feasible solution where at least one basic variable equals zero.
Takeaway: Degeneracy can make simplex cycle; Bland's rule stops it.
Quick check: Can the simplex method keep pivoting forever without reaching the optimum?
- No, it always improves
- Only if infeasible
- Yes, through cycling
Degenerate pivots can cycle; Bland's rule prevents it.
DegeneracyBland's rule
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