I have always seen inequality constraints for optimization problems written as less than or equal to 0 (such as $Ax\leq0$). However, in a book I was reading, throughout they give inequality constraint as being less than or equal to 0 (for example $\mathcal{W}=\left\{w \mid Vw\leq1\right\}$).
I was wondering if there is a reason to write it this way. I get that $Ax-b\leq0$ is the same as $Ax\leq b$ which you could normalize to $Cx\leq 1$. But is there anything more specific being conveyed by writing it this way?
Link to book (purchase link but may be able to access through academic library): MPC.
The standard form of inequality for MPC is $\mathbf{A}\mathbf{x}\le\mathbf{b}$.
In a special case when $\mathbf{b}=\mathbf{0}$, it turns into $\mathbf{A}\mathbf{x}\le\mathbf{0}$.
The case $\mathbf{C}\mathbf{x}\le\mathbf{1}$ is a trivial conversion. Let's assume every $i^{th}$ row of matrix $\mathbf{A}$ is shown by $\mathbf{A}_i$, then
$$\mathbf{C}_i=\frac{\mathbf{A}_i}{b_i}$$ It is possible when no element from $\mathbf{b}$ is equal to zero.