Maxima and minima

What is it?

Formulas

$$f(x^\ast) \le f(x)\ \ \forall x$$

$x^\ast$ is a global minimum

$$\exists\delta > 0:\ f(x^\ast) \le f(x)\ \ \forall x,\ |x - x^\ast| < \delta$$

$x^\ast$ is a local minimum

Where it shows up in computing

• Operations research and logistics★★★★★fundamentalOptimization and systems

  Cost minimization and profit maximization are the native language of operations research.

Where it shows up in AI

• Loss function★★★★★fundamentalAI and machine learning

  Training is the search for parameters that minimize the loss — in practice, a good local minimum.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

What depends on it

• Critical points and derivative tests
• Constrained optimization