# Cyclic descent

### From Glossary

An algorithm that seeks to optimize a multivariate function by optimizing each coordinate with a univariate optimization technique (keeping the other coordinates fixed). This is repeated until a fixed point is reached. In general, it is possible for such a fixed point not to be an optimum (even locally) because a simultaneous change in variables could result in an improvement. An example is given by:

has a minimum at , and has a minimum at . However, decreases with simultaneous change, . Along this parabola, , which is negative for nonzero. Thus, is not a local minimum of . For further discussion about this example, see Myths and Counter Examples.