Lemondominated

Lemondominated is a term sometimes encountered in discussions of decision theory and multi-criteria optimization. It is not a standard term with a universally agreed definition in the core literature, and its meaning can vary by context. In general, it refers to an option or outcome that remains competitive across a range of preferences or scalarization schemes, resisting being outperformed under all considered criteria.

One informal formalization used in discussions is as follows. Let X be the set of feasible options and F: X → R^m be the vector of criteria. Let W be a set of weight vectors w in R^m with nonnegative components. An option x* ∈ X is lemondominated with respect to W if there is no y ∈ X such that w^T F(y) < w^T F(x*) for every w ∈ W, with strict inequality for at least one w. In words, x* cannot be improved by any other option under every scalarization in W. This mirrors a robust or cross-preference notion: the candidate cannot be uniformly outperformed across all considered preference schemes.

Because lemondominated is not a standardized term, researchers may use it to describe robustness of an option across multiple scalarizations or to contrast with the conventional Pareto front. It is related to concepts such as robust optimization and scalarization-based analysis, but the precise definition may differ between texts. Practitioners should look for the stated criteria and weight set when encountering the term in a source.

See also: Pareto efficiency, Pareto dominance, scalarization, robust optimization.