local maximum

A local maximum for a function is a set of parameters for the function that give the largest output in a neighbourhood, that is f(p) > f(p+δ) for small changes δ in the parameter value. In a physical landscape this would correspond to the top of a small hill, but where there may be a much larger hill elsewhere. It is the opposite of a local minimum and is to be contrasted with a global maximum which is the largest/highest point overall.

This geographic analogy can be helpful in the case of the fitness landcape generated by a fitness function for machine learning. However, whilst the space of parameters for a physical location is 2D (latitude, longitude), the space of parameters of a fitness functoon is often multi-dimensional and may include a mix of different kinds of parameters, not just numeric.