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]
168 questions
9
votes
5 answers
Find a ternary $4\times 39$ matrix satisfying the conditions below
Can you find a matrix $A_{4\times39}$ with elements from $\{-1,0,1\}$ so that
No column is all zero.
All columns are different.
No column is $-1$ times another column.
Each row consists of $13$ of each of $\{-1,0,1\}$.
How can you do that? Is it…
juliet
- 359
8
votes
3 answers
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
- 403
6
votes
0 answers
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
- 89
5
votes
1 answer
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
- 113
5
votes
2 answers
Creation/computation of "Two not touch" puzzles
This is a mathematical and algorithmic question, so I hope it is not flagged for failing to be a pure mathematical question.
The puzzle "Two not touch" (or Star Battle) consists of a $10 \times 10$ grid array fully tiled with irregularly shaped…
David G. Stork
- 30,409
5
votes
1 answer
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
- 463
4
votes
0 answers
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
- 795
4
votes
1 answer
What Is The Most Efficient Way To Tile A Page With Cube Nets?
I'm trying to print out nets of a cube on a sheet of paper, and I'm hoping to fit as many as I can on single sheets. The squares that make up the net are $\frac{1}{2}$ an inch wide, and I'm printing on standard 8.5" x 11" printer paper. I know that…
JavamonkYT
- 75
4
votes
0 answers
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
- 41
4
votes
0 answers
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
- 964
4
votes
0 answers
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…
3
votes
1 answer
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
- 797
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3
votes
1 answer
Demonstrating Piecewise Linearity in a Parametrized Optimization Solution
Let $\mathbf{B}$ be a definite positive square matrix of size $n \times n$, and $\mathbf{b}$ an $n$-sized vector. It can be shown that the solution of $\arg\min_x \left(\mathbf{x}^T \mathbf{B} \mathbf{x} - 2\mathbf{b}^T \mathbf{x}\right)$ is…
cyril
- 33
3
votes
1 answer
Social golfer problem with additional requirement
I need to write a program that sorts people into groups.
To give a little context: The aim of the program is to create an equitable distribution of tasks and people for a school trip. Every day the groups are reshuffled and each group is assigned a…
3
votes
5 answers
Do perfect squared rectangles with corners of sizes 10, 12 and 13 exist?
A squared rectangle is a rectangle dissected into squares.
squared rectangles are called perfect if the squares in the tiling are all of different sizes and are positive integers.
The smallest perfect squared rectangle is 33x32 in width and height.…
Stuart Anderson
- 109