I have three variables $x_{1},x_{2},x_{3}$ and a function $f : D \rightarrow \mathbb{R}$ where $D$ is defined as such :
$$D = (x_{1},x_{2},x_{3})$$ such that $$x_{1}+x_{2}+x_{3}=1$$ and $$x_{1}>x_{2}>x_{3}$$ Therefore, D is the intersection of a plane and a box, and hence is a plane.
The objective is to find $(x_{1},x_{2},x_{3}) \in D$ such as $f(x_{1},x_{2},x_{3}) = c \in \mathbb{R}$. The function $f$ is injective and so for a fixed $c \in \mathbb{R}$, there can be multiple solutions $(x_{1},x_{2},x_{3})$. Among all the solutions, I want to find the one that has the highest $x_{1}$, and then once the highest $x_{1}$ is found, the highest $x_{2}$. How do I specify this constraint ?
Note that the function $f$ doesn't have a closed-form solution and I am using minimize from scipy to find the $(x_{1},x_{2},x_{3})$.