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If I understand correctly, you can obtain the desired linear constraints via conjunctive normal form. Explicitly, suppose $f(\bar{x}_1,\dots,\bar{x}_n)=1$, and let $S_0 = \{j\in\{1,\dots,n\}:\bar{x}_j = 0\}$ and $S_1 = \{j\in\{1,\dots,n\}:\bar{x}_j = 1\}$. You want to enforce \left[\left(\bigwedge_{j\in S_0} \lnot x_j\right) \bigwedge \left(\bigwedge_{j\... 1 {0,1}-ILP can be rewritten as Pseudo-Boolean programming or MAX-Sat. It might be worth to explore alternative solving technologies for your problem. 3 You are not going to be able to add these logs and quadratic terms to the model via simple double-sided big-M constraints, as they generate non-convex use of convex quadratics and logs, and CVX does not support that. The use of the squared log is not possible either. I don't think it supports automatic modelling of nonconvex use of abs operator either. Most ... 6 If I understand correctly, the following enforces your desired behavior: \begin{align} y_1 &= d_1 \\ y_2 &= d_2 \\ y_3 &= d_3 \\ y_4 &\ge d_1 + d_2 - 1\\ y_5 &\ge d_1 + d_2 + d_3 - 2\\ \end{align} If you also want to enforce y_4 \implies (d_1 \land d_2) and y_5 \implies (d_1 \land d_2 \land d_3), then include these additional ... 4 Suppose we know an upper bound M for y such that |y| \leq M, we can linearize this constraint as follows. First, we introduce a new variable h \in \mathbb{R} with h = b y. Then we need to model that h equals y if b = 1 and equals 0 if b = 0. For this purpose we add the following linear constraints: \begin{align} h &\leq b M \tag{1} ...