set-valued analysis

Set-valued analysis is a branch of mathematics that studies functions which assign a set of values to each point in a domain, rather than a single value. Think of it like a machine where, for each input, you get a bundle of possible outputs instead of just one. This approach helps in understanding complex systems with uncertainty, constraints, or multiple outcomes, such as in optimization, control theory, and economics. It provides tools for analyzing how these sets change smoothly or abruptly as the input varies, helping us understand behaviors in complex, real-world situations.