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Although focused on implementing the model in YALMIP instead of CVX (converting the code should be trivial), precisely this case is described in the following tutorial https://yalmip.github.io/modelli …

My interpretation is that you want $y$ to be $i$ if $p_i=1$. You can do that with a simple multiplication $y=c^Tp$ where the constant vector $c$ is given by $c_i=i$.

By Farkas lemma, infeasibility of $Ax\leq b$ is equivalent to feasibility of $A^Ty = 0, y^Tb < 0, y\geq 0$, or more practically useful $A^Ty=0, y^Tb \leq -1, y\geq 0$. Unfortunately, this will lead to …

In YALMIP you can use arbitrary black-box operators to circumvent modelling n = 5; c = randn(3*n,1); A = randn(10*n,3*n); b = rand(10*n,1); % MILP model x = sdpvar(2*n,1); Domain= [0 <= x <= 1]; % Bi …

As all have mentioned, the problem is intrinsically hard, as it effectively involves a strict inequality. One way to represent it, using no strict inequalities or magic constants, is to use the simpl …

Consider maximizing $\sum_{i=1}^n x_i$ subject to $x$ binary and $\sum_{i=1}^n i x_i \leq 2$ Solve relaxation and it gives $x_1 = 1, x_2 = 1/2$ with remaining variables 0. Branch on $x_2 = 0$ and the …

You can ask Gurobi to do this for you https://www.gurobi.com/documentation/9.1/refman/preqlinearize.html Whether a linearization leads to better or worse performance is almost impossible to know befor …

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 n …

Introduce a term $y_m$ to replace and lower bound the terms inside the logarithm. Those lower bound constraints simplify to $\sum_{n=1}^{N}(1-x_{m,n})\omega_{m,n}+z\ge y_m(\sum_{n=1}^{N}x_{m,n}\omega_ …

You just seem to have hidden a long list of constraints of the form $(x_i=j) \Rightarrow \text{equalities}_{ij}$ Introduce a binary matrix $C_{ij}$ with $\sum_j C_{ij}= 1$ and $C_{ij} \Rightarrow \{x …

Introduce a binary variable $\delta_t$ to represent which case it is and $z_t$ to represent the modelled product, and your MILP model of the piecewise-affine dynamics would be ${EP}_t\ =\ \sum_{i=1}^{ …