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1500 questions
4
votes
1 answer
How do we branch a Cutting Stock problem using Branch and Price?
I'm sure this is a straightforward question, but since I started learning integer programming recently this isn't clear to me.
Consider solving a 1 dimensional cutting stock problem using delayed column generation / branch and price. You start by…
133crem
- 41
- 2
4
votes
1 answer
Endowment of an agent
I was going through the Shapley-Folkman-Starr Lemma (https://simons.berkeley.edu/sites/default/files/docs/3605/simons2.pdf) and I came across the term "endowment" of an agent.
My assumption is that it represents a (sub)set of the agent's preferred…
user12632521
- 111
- 4
4
votes
0 answers
Analytical solution of constrained quadratic program
I'm trying to solve a "simple" (= small) optimization problem often, with only minor changes to the objective function. Therefore it's important to keep the "time per solve" as low as possible. This problem is basically a QP with $Q :=…
kchnkrml
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- 2
4
votes
1 answer
Do my constraints to restrict the splitting of tasks make sense?
I have a problem where there are stations, types and tasks which has to be assigned to each other. Now for me the thing is I want the variable $x$ to be not binary like in assignment problem for example but between $[0,1]$. Now I wanted to add a…
Harun Gül
- 49
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4
votes
1 answer
Canonical Form of Mixed Integer Program
I could use some help understanding what's going on here. Admittedly, I am not strong in OR, but I don't fully understand the format shown below. Is it possible somebody could format this in the type of notation that is more often found in…
Imdum
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4
votes
1 answer
Finding a dual feasible basis for use with the dual simplex algorithm
I have learnt that the dual simplex method requires reduced costs to be non-negative or else it cannot be used.
I wanted to know what could be done to find a dual feasible basis and came across this related (if not identical) question in the math…
Ram
- 137
- 4
4
votes
1 answer
Bounding function for branch-and-bound in game tree search
The scenario is a game where each round you can buy or sell farms that make a set profit each round. I thought about applying branch-and-bound to a game tree, where each node represents the game state after each round, after buying/selling. The…
qwr
- 141
- 2
4
votes
1 answer
Creating constraints dynamically in pyomo abstract model
I have a networkX graph with few nodes and these nodes have attributes such as "demand".
def mygraph():
G = nx.Graph()
G.add_nodes_from([("N1", {"demand": 10}),
("N2"{"demand": 12}),
("N3", {"demand": 25}),
("N4"{"demand":…
Waqas Swati
- 69
- 7
4
votes
1 answer
Is this a non-linear integer model?
Let's say if I have two decision variables, $f$ and $g$ respectively, where $f$ is continuous, and $g$ is binary.
If I have a constraint like this,
$$ f\cdot g \le C$$
Does this make my model nonlinear or quadratic integer model?
overboxed
- 593
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4
votes
2 answers
Attempting to define dual crossover for barrier optimization in CPLEX
I am exploring what the tradeoffs are between no crossover, crossover w/ default settings, and crossover with just dual for barrier optimization.
When I attempt to define my solver settings for the crossover with dual, I thought, based on the CPLEX…
JBH_84
- 61
- 4
4
votes
3 answers
How do you get the primal solution of an LP from the dual solution?
I am new to Optimization so I think the following question may be very easy, but I'm not sure how to solve it.
The dual of an LP is an LP. If we solve the dual LP, we can get the optimal value for the primal problem. But:
How do we get the optimal…
Helix
- 141
- 4
4
votes
3 answers
Is it better to use GAMS or Python for Optimization Models?
I have been using GAMS for several years, and I would like to do my new research in Python programming language. It is simple to do coding stuff in GAMS, however, it takes much time in complex optimization models.
I usually do NLP and MILP.
dozgunay
- 139
- 5
4
votes
0 answers
Expected Value of Piecewise Exponential Function
I have the following distribution.
$$\operatorname{logpdf}(x) = -\sum_{i = 0}^n \max(v_i \cdot x + b_i, 0) -1/2 (x - \mu)^T M (x - \mu) + \text{const}$$
Where $M$ is symmetric positive definite, $x \in \mathbb{R}^m$, with $m$ around $500$ and $n$…
JEK
- 121
- 2
4
votes
1 answer
How to find such a Markov matrix?
Suppose $A$ is a $m\times n$ Markov matrix, and $C$ is a $m\times k$ Markov matrix. How to decide (analytically or numerically) whether there is a $n\times k$ Markov matrix $B$ such that $AB=C$? I feel that it is a question of feasibility in linear…
Ypbor
- 163
- 2
4
votes
1 answer
'Solving' an optimization problem
This might be a silly question but by 'solving' an optimization problem do we mean if an optimal solution exists we find such a solution and its optimal value and if it 'doesn't exist' (for example the optimal solution is $\pm\infty$ or there is no…
Emad
- 183
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