Largimin

Largimin is a term that appears in a range of mathematical and theoretical discussions but does not have a single, universally standardized definition. In many informal or introductory contexts, largimin is used to refer to concepts that combine the ideas of largest values and minimums, and its precise meaning can vary depending on the source.

In decision theory and game theory, largimin is sometimes treated as synonymous with the maximin value: the best of the worst-case outcomes for a given set of strategies. For example, in a simple payoff matrix, if strategy A has a worst-case payoff of 1 and strategy B has a worst-case payoff of 2, the largimin (as maximin) would be 2.

In other usages, largimin is defined as a straightforward operation on a set of lower bounds: largimin(l1, l2, ..., ln) = max(l1, l2, ..., ln). This interpretation treats largimin as the largest among several guaranteed minimum values. For instance, with lower bounds 0.3, 0.45, and 0.4, the largimin would be 0.45.

Etymologically, the term is a portmanteau of “largest” and “minimum.” Because it is not standardized, researchers and writers may adopt different definitions for largimin depending on context, field, or personal convention. When encountering largimin in literature or notes, it is advisable to check the source’s specific definition.

See also: maximin, minimax, robust optimization.