In optimization, what is a "local minimum"?

A "local minimum" refers to a point in a function where the value is lower than all other values in its immediate vicinity or neighborhood, while not necessarily being the lowest point overall in the entire range of possible values. In mathematical terms, a local minimum is a solution that is optimal within a limited region but may not represent the best overall solution when considering the entirety of the function.

This makes the choice regarding the lowest solution in the neighborhood correct. It highlights the concept that local minima can exist within a larger context where there might be lower points elsewhere, sometimes called a "global minimum."

The other options describe concepts that do not align with the specific definition of a local minimum. The "best solution of the entire range" refers to a global minimum, which is distinct and represents the absolute lowest point across the whole function. The "highest feasible solution" would pertain to maximization problems rather than minimization and does not apply to this context. Lastly, an "average solution" does not relate to the concept of minima in the least bit, as it suggests a mean value rather than focusing on extremal values in optimization.