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A solution <math>x^*\in X</math> (and the corresponding outcome <math>f(x^*)</math>) is called Pareto optimal if there does not exist another solution that dominates it. The set of Pareto optimal outcomes, denoted <math> X^* </math>, is often called the '''[[Pareto front]]''', Pareto frontier, or Pareto boundary.
The Pareto front of a multi-objective optimization problem is bounded by a so-called '''[[nadir]] objective vector''' <math> z^{nadir} </math>and an '''ideal objective vector''' <math> z^{ideal} </math>, if these are finite. The nadir objective vector is defined as
:<math> z^{nadir} = \begin{pmatrix}
\sup_{x^* \in X^*} f_1(x^*) \\
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