Top new questions this week:
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Consider the following situation. I have an integer program which I want to solve using column generation. After a suitable decomposition, the master problem has decision variables that select the ...
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I solve a nonlinear optimization problem of the form
\begin{align}
&\max x_0 \text{ such that } \\
&\left[ \sum_{j=0}^N \left(\alpha_j x_0^{j} \prod_{k=3}^j x_k \right)\right]^2 + \left[ \...
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I'm working on a problem with the following formulation:
\begin{align}
\min&\quad\sum_{i \in N} \sum_{j \in J} V_{ij}x_{ij}
\\
\text{s.t.}&\quad \sum_j x_{ij} = 1 \quad \forall i \in N\\
&...
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Let $G$ be a graph with a set of nodes $V$ and a set of edges $E$.
Let $G'$ be a graph with the same set of nodes $V$ but a second set of edges $E'$.
For a set of nodes $X\subset V$, we denote $f(X)$ ...
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Consider a Geometric Program (GP),
$$
\begin{array}{cl}
\operatorname{minimize} & f_{0}(x) \\
\text { subject to } & f_{i}(x) \leq 1, \quad i=1, \ldots, m, \\
& g_{i}(x)=1, \quad i=1, \...
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I face a feasibility problem of type
$$ c_i(\boldsymbol x) \leq 0, i = 1, \dots, \mathcal{I} \\ c_e(\boldsymbol x) = 0, e = 1, \dots, \mathcal{E} $$
where $\mathcal{I} + \mathcal{E} \gg \text{dim}(\...
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As stated in this paper, there is a technique to reformulate a multi-commodity flow problem (MCF) with undirected edges to its equivalent version with directed edges.
By quoting them:
The ...
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Greatest hits from previous weeks:
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The terms "soft constraints" and "hard constraints" are used in the context of optimization modeling.
Is there any standard way to figure out which is which in some of the complicated models?
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Is anyone aware of a medicine/vaccine related challenges with a good problem definition and some available input datasets, ideally related to COVID-19? What kind of constraint solving challenges would ...
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For the TSP there famously is the concord solver (http://www.math.uwaterloo.ca/tsp/concorde.html) which is argubly the fastest exact solver for the TSP.
There are many other problems that also show ...
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As part of a final project for my linear programming course, I have been asked to discuss implementations of pivot algorithms, including which combinations of the ideas we have talked about in class ...
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I know that there are some questions concerning this type of error, for example, this link.
I first installed the latest version of ipopt through command line into my Pyomo environment and got the &...
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This semester I will start teaching Programming in Python to Master students in Supply Chain Management.
I would like to start the first lesson with "Why learning programming languages will be useful ...
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In the (famous) Trolley Problem (https://en.wikipedia.org/wiki/Trolley_problem) - a runaway train is out of control and unfortunate people are stuck on two different railway tracks. The railway ...
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Can you answer these questions?
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I am trying to model a MILP, where in the objective, the product of two variables is introduced. This is solved through the introduction of a new variable according to the following logic:
"...
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I have a MILP problem that requires knowing the number of nodes within a cycle (there will be multiple depending on inputs). I believe this will involve tracing nodes/values within cycles using the ...
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I solve a nonlinear optimization problem with constraint
$$ \sum_{j=1}^S \ln \Bigg( \Big(1 -x_j c_k + y_j d_k\Big)^2 + \Big( x_j d_k + y_j c_k \Big)^2 \Bigg) \leq 0, \: k = 1, \dots , K $$
where the ...
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