# Tag Info

Accepted

• 21.7k
Accepted

### If $x=\min\{f(\mathbf{a}),1-\epsilon\}$, how can we model and partition $x$?

Start with the constraints $$x \le f(\mathbf{a})$$ and $$x \le 1-\epsilon.$$ If the nature of the problem is that larger values of $x$ are always preferable in objective terms to smaller values of $x$,...
• 28.8k
Accepted

### Linearizing $y=\sum_{i=1}^n(z+c)\left(\frac{r_i^2}{1-r_i}\right)\phi_i$

You are on the right track. Linearizing the product of a continuous variable ($\xi_i$) and a binary variable ($\phi_i$) is a FAQ. See, for instance, How to linearize the product of a binary and a non-...
• 28.8k
I will first formalize the described problem in mathematical notations, I think it is more suitable, rather than a piece of code, for providing a better understanding. So, let $B$ be the brands set; \$...