Cunningham's Rule constructions because they tend to average out how many times a variable pivots. It has recently been shown by David Avis and Oliver Friedmann that there is a family of linear programs on which the simplex algorithm equipped with Cunningham's rule requires exponential time. Cunningham's Rule In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed 1979 by W.H. Cunningham to defeat the deformed hypercube constructions by Klee and Minty et. al. (see, e.g. Klee–Minty cube). Cunningham's rule assigns a
Zadeh's Rule Programming and Combinatorial Optimization conference in 2011 by Oliver Friedmann. Zadeh, although not working in academia anymore at that time, attended the conference and honored his original proposal. Zadeh's Rule In mathematical optimization, Zadeh's rule (also known as Least-entered rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed around 1980 by Lotfi A. Zadeh, and has entered the folklore of convex optimization since then. Zadeh offered a reward of $1,000 to anyone who can show that the rule admits polynomially many iterations or to prove that there is a family of linear programs