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
General Leibniz rule General Leibniz rule In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if formula_1 and formula_2 are formula_3-times differentiable functions, then the product formula_4 is also formula_3-times differentiable and its formula_3th derivative is given by where formula_8 is the binomial coefficient and formula_9 This can be proved by using the product rule and mathematical induction. If, for example, , the rule gives an expression for the second derivative of a product of two functions: The formula can be generalized to the product of "m"