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5

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\...


5

There is a good reference that has been published by Alireza Soroudi. Power System Optimization Modeling in GAMS


3

The state-of-the-art method for solving the vehicle routing problem with split deliveries is in fact LBBD as can be seen in the following papers: https://www.sciencedirect.com/science/article/abs/pii/S037722171400352X https://pubsonline.informs.org/doi/abs/10.1287/trsc.2018.0825 Although the authors do not refer to their algorithms as LBBD, their methods can ...


2

For the case of mixed integer programs, I would recommend the following paper: Klotz, E., & Newman, A. M. (2013). Practical guidelines for solving difficult mixed integer linear programs. Surveys in Operations Research and Management Science, 18(1-2), 18-32. As the abstract says: "Even with state-of-the-art hardware and software, mixed integer ...


3

There's also the Octeract Reformulator repository, where we host a growing collection of scripts to automatically apply reformulations to non-linear problems, e.g.: from octeract import * # Linearize bilinear term x*y where x,y binary # ============================================= # x*y = w # w <= x # w <= y # x + y - 1 <= w # 0 <= w <= 1 # ...


3

I would also add "Optimization in Engineering" as a reference. It offers a good overview on LPs, MILPs and convex programming, focusing on applications. It is also a good resource in best practises, see for example Chapter 3.3 "Linearizing Nonlinearities Using Binary Variables".


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