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
Chain rule a variable "z" depends on the variable "y", which itself depends on the variable "x", so that "y" and "z" are therefore dependent variables, then "z", via the intermediate variable of "y", depends on "x" as well. The chain rule then states, The two versions of the chain rule are related; if formula_4 and formula_5, then In integration, the counterpart to the chain rule is the substitution rule. The chain rule seems to have first been used by Gottfried Wilhelm Leibniz. He used it to calculate the derivative of formula_7 as the composite of the square root function and the