What does a "local maximum" refer to?

A "local maximum" refers to the best solution within its immediate neighborhood or vicinity. In the context of optimization, particularly in mathematical and economic modeling, a local maximum is a point where the function value is higher than that of its surrounding points, but it does not necessarily mean it is the highest point in the entire solution space.

To understand this concept, consider a hilly landscape where you may find a peak that is higher than all the surrounding areas immediately around it; however, there could be another, taller peak elsewhere in the landscape. The local maximum in this analogy represents that immediate peak, while a global maximum would be the highest peak in the entire landscape. Recognizing local maxima is important in optimization problems since they can provide valuable insights or solutions that are efficient, even if they aren't the best overall solution.