All Questions
Tagged with applications optimization
44
questions
16
votes
1
answer
5k
views
What are the use cases of the Dirichlet energy in computer vision?
I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What ...
user168764
13
votes
2
answers
3k
views
Using math for interior decorating with lamps
When I was in college, I owned three lamps and had a dark apartment. I kept trying to position them in different areas of the room, but it was still dark. Then I decided to model the problem with math:...
- 13.3k
10
votes
2
answers
352
views
Applications of Linear Programming to pure mathematics
This semester I'm taking a course in Linear Programming. While the topic is very interesting, all the applications I can find about this topic seem to be outside of mathematics. What are some ...
- 457
10
votes
1
answer
495
views
Nontrivial applications of tropical mathematics to optimization (soft question)
I have been looking into tropical algebra/geometry for a research problem I'm working on in optimization. Tropical math gets referenced a lot in the literature, but it seems to me that its mostly just ...
- 395
8
votes
1
answer
125
views
What is the best shaped blanket for my bed? (minimizing average work done in pulling it up when it falls off)
When my blanket is hanging off the bed, it's difficult to pull it up again. The more that hangs off, the harder it is; as we learn in calculus, pulling up the first half of the way is three times ...
- 13.3k
7
votes
2
answers
866
views
How can I, as a future mathematician, contribute most to Smart Grid research?
After I've finished my Master's degree in mathematics, I too want to use my powers for good.
One endeavour I consider good is the pursuit of the design and implementation of a Smart Grid which will, ...
- 7,148
7
votes
2
answers
2k
views
Optimization Puzzle
You are given a large number of LEGO blocks of size 1. You can build blocks of other sizes using smaller blocks. For example, you can build a block of size 2 using two of size 1 blocks and then build ...
- 201
6
votes
1
answer
104
views
Minimize travel time of a group of people with a motorbike
Problem: A group of $n$ people ($n\geq2$) want to travel from A to B but they can only either walk or use a motorbike (fit 2 people) [note that there is exactly $1$ motorbike for them to use]. Given ...
5
votes
1
answer
723
views
Who knows Krotov's Method in Optimal Control Theory
I'm finishing my PhD thesis about applications of optimal control
theory in the field of energy harvesting. In the course of my PhD I dealt with different ways to compute optimal controls, and I found ...
- 816
3
votes
2
answers
127
views
How are the functions determined for real-world applications (business, population models, etc.) of calculus?
The following problem has been taken from Paul's Online Notes:
"We need to enclose a rectangular field with a fence. We have 500 feet of fencing material and a building is on one side of the ...
- 33
3
votes
1
answer
482
views
Building a highway at the minimum cost
I am asked the following question:
You are responsible for building a highway that connects A to B. There's an old highway 50 miles south that can be restored at the cost of \$300.000,00 per mile. ...
- 1,927
3
votes
1
answer
284
views
Estimation of $\lambda$, $\mu$, and $\sigma^2$ given observations of $Z=X+Y$, $X\sim\text{Poi}(\lambda)$, $Y\sim\mathcal N(\mu,\sigma^2)$
Let $X\sim\operatorname{Poisson}(\lambda)$ and $Y\sim\mathcal N(\mu,\sigma^2)$ be independent and define $Z=X+Y$. The density of $Z$ can be described as an infinite Gaussian mixture of the form
$$
f_Z(...
- 6,127
3
votes
3
answers
289
views
Applications of chemical reaction networks
I have recently read a bit on chemical reaction network theory. I was wondering whether the mathematical concepts have cross-field applications like neural networks. For example, can I apply chemical ...
- 306
3
votes
1
answer
3k
views
Real Life Optimization Problem
You are given a set $A$ of integers of size $n$ and a common divisor $r$ called the "anchor", which isn't in $A$ and isn't necessarily the greatest common divisor, either. Let $M$ be the least common ...
- 201
3
votes
0
answers
30
views
Projection of sparse weighted graph into $\mathbb{Z}$
Problem statement in the title is simplified and this question is actually quite open-ended: I have a sparse undirected simple weighted graph $G$ and need to find an injective function $G \rightarrow \...
