About correct notation of pareto dominance in optimization

Question

I search the correct notation of Pareto Dominance, but i don't know if it is a question for Mathexchange or here..

In multiple papers, like the classic Deb nsga2 paper, you can found the pareto dominance relation written like this

A dominate B if

In wikipedia, or other paper, like this one of Zitler, you find another notation :

A dominate B if

What is the best and correct mathematic notation here ? What is the exact name of this symbol ?

Answer 1

≺ is called precedes, ≻ succeeds.

According to the well known Evolutionary Optimization Algorithms the standard notation for A dominates B is A ≻ B:

20.1 Pareto Optimality

[...]

Domination: a point x^* is said to dominate x if the following two conditions hold:

1. f_i(x^*) <= f_i(x) for all i ∈ [1,k]
2. f_i(x^*) < f_i(x) for at least one j ∈ [1,k]

that is x^* is at least as good as x for all objective function values and it's better than x for at least one objective function value. We use the notation:

x^* ≻ x

to indicate that x^* dominates x.

This notation can be confusing because the symbol ≻ looks like a "greater than" symbol but since we deal mainly with minimization problems, the symbol ≻ means the function values of x^* are less than or equal to those of x.

However this notation is standard in the literature, so this is the notation that we use.

However even the reverse notation is used (probably "to avoid" the confusion the author refers to!)