Constraint programming is a particular form of optimization modeling that tends to be well-suited for combinatorial models like scheduling and planning.

# Questions tagged [constraint-programming]

141 questions

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votes

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### Is group theory useful in any way to optimization?

For what I have seen, optimization uses a lot of linear algebra and convex analysis, but I have not seen any group theory being used, so I was curious about it.
Is group theory useful in any way to optimization?

rnegrinho

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### mathematics of chemical stoichiometry

I would like to better understand the mathematical description of chemical stoichiometry and thermodynamic chemical equilibrium. This problem has many features and I know my description might be too vague.
There are generally two approaches to the…

jpantina

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### Merit function vs Largrange Functions vs Penalty Funcitons

I've been reading up on constraint optimization. I've come across the three terms:
Merit Function
Lagrange Function
Penalty Function
I'm pretty sure all these three things are the same. That is, they quantify how much an iterate satisfies both the…

echo

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### A problem on 0-1 matrices.

Given a 0-1 matrix $A$, is there an efficient way to find all 0-1 vectors $x$ such that $Ax = v$ where the entries of $v$ belong to a set $\{a,b\} \subseteq \mathbb{Z}$ of size $2$?
Note that $v$ is not a fixed vector, it can vary over all $2^n$…

Anurag

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### On the "solvability" of jigsaw Sudoku puzzles

I am making a computer program that is going to generate Sudoku puzzles of various types. One of these types is "jigsaw", in which the board is split into rows, columns and random 9-square contiguous regions. My regions are generated completely…

maxG795

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### projection from a point to a constrained hyperplane

I am trying to find the closest point on the following constrained hyperplane to a general point $\vec x$ :
$$ \vec \omega \!\cdot\! \vec 1 = 1 \ \ s.t \ \ \alpha_i \le\omega_i\leq\beta_i $$
$$ 0\leq\alpha_i\lt\beta_i\leq1$$
I have projected $\vec…

shan

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### Is Lester Ingber theory for real?

I am not sure whether to ask this in Physics, Math, or Computer Science, but I will try Math.
I read a paper "Nonlinear nonequilibrium statistical mechanics approach to C3 systems." Lester Ingber. 9th MIT/ONR Workshop on C3 Systems: Naval…

Tyler Durden

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### Comparison of constrained optimization methods

I am trying to solve a constrained optimization problem using filter methods and came across two papers on the topic that I am having some problems with. The original filter method paper is the following: Fletcher & Leyffer (2002) and the paper I…

RustyStatistician

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### Trace minimization subject to constraints

I have seen in an article that
$ \min_{\mathbf{K}} \hspace{0.2cm} tr[\mathbf{K} \Sigma \mathbf{K}^T]$
s.t. $ \mathbf{KH} = \mathbf{I} $
where $\mathbf{H}$ is of full column rank yields,
$\tilde{\mathbf{K} } =…

shani

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### How to take the partial derivative of $f(x,y) = x\ln(x) + y\ln(y), x + y = 1$?

Let $f(x,y) = x\ln(x) + y\ln(y)$ be defined on space
$S = \{(x,y) \in \mathbb{R}^2| x> 0, y > 0, x + y = 1\}$.
My question is, how do I take the partial derivative for this function, given that the parameters are coupled through $x+y = 1$.
A first…

Concu Bine

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### Number of ideals with GAP

Let $A=K\langle x,y\rangle$ be the polynomial in non-commuting variables $x,y$ over a finite field $K$ with $q$ elements and $J=\langle x,y\rangle$ the ideal generated by $x$ and $y$.
I want to find all ideals I having the property that $J^4…

Mare

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### Constraints on a matrix

I have a matrix equation of the form $A \times B = C$.
$A$ is an $n \times m$ matrix. $B$ is an $m \times 1$ matrix. $C$ is obviously $n \times 1$.
Here are the constraints:
All values are positive and between 0 and 1 inclusive.
$C$ is given…

Learning...

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### How to reduce the number of (overlapping) constraints in a linear program?

I am trying to solve a linear program with more than 7 million constraints which could not be solved on my computer (In total around 5000 variables). In the constraints there is a overlap between them. For example:
$2X_1 + 3X_2 \leq 5$ and
$1X_1 +…

Tobias Dekker

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**1**answer

### Number of orderings with tree-based constraints

How can I compute the number of possible orderings of the numbers $1,\dots,N$, where some constraints are given on the relative order of some numbers?
I know how to do the calculation in simple cases. For example:
If the constraints are that $7…

Erel Segal-Halevi

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votes

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### Expressing problems in canonical form for solving with simplex

The Picnic Hamper Company has a store containing 10,000kg of nuts, 4000
packs of smoked salmon, 2000 bottles of wine and 1500 Victoria sponges.
It intends to use these goods to make up three different sorts of hampers
with contents and price as…

lary

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