Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

In multicriteria optimization problems appart from the notion of Pareto optimality there is also the term weakly Pareto optimality. For that case, the definition is that

A feasible solution $\hat{x} \in \mathcal{X} \quad$ is called weakly efficient if there is no $x \in \mathcal{X} \quad$ such that $f(x) < f(\hat{x})$, i.e. $f_k(x) < f_k(\hat{x}) \quad \forall k = 1, \ldots , p$.

Notice that the Pareto optimal set is a subset of the weakly Pareto optimal set.

I wonder the practical importance of the weakly Pareto optimal set. Do you any situation where they are important?

share|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.