All Questions
Tagged with applications optimization
44
questions
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 ...
2
votes
1
answer
115
views
Standard definition of a game in game theory
Sorry for my naive question, but at the moment I can't quite figure it out.
I'm consulting various documents on game theory in order to get the standard definition of what a game (and an associated ...
- 8,424
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 ...
- 8,424
16
votes
1
answer
5k
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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 ...
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 ...
- 80
2
votes
0
answers
127
views
Examples of a gradient flow
Suppose we have a gradient flow in $\mathbb{R}^n$ :
$$\frac{d}{dt}x(t)=-\nabla F(x(t)), \qquad x(0)=x_0.$$
where $F : \mathbb{R}^n \to \mathbb{R}$ and $x : \mathbb{R}_+ \to \mathbb{R}^n$. What are ...
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
1
vote
0
answers
25
views
Strategies to find the best basis function on a Hilbert space
Consider the Hilbert space associated with the $L^p$-norm. I'm interested to find the best (in the sense of the most sparse) truncated approximation for isomorphic functions in this space. Naturally, ...
- 165
2
votes
1
answer
46
views
Applications of SGD outside learning tasks
Are there applications, outside of machine learning, where stochastic gradient descent (SGD) is the preferred method of optimization?
By SGD, I mean any first-order method which approximates the true ...
- 4,411
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 ...
- 102
0
votes
0
answers
51
views
Application of differentiation based on electricity consumption
A utility company has a small power plant that can produce a kilowatt hours of electricity daily at a cost of 10 - (𝑥/10^5) cents each for 0 < x < 8 x 10^5. Consumers will use 10^5(10 - p/2) ...
- 9
1
vote
1
answer
1k
views
Optimisation Problem for Pipe Nesting
I work in a company where we are supposed to produce and send pipes using trucks to buyers. Pipes of smaller diameter can be nested inside pipes of larger diameter while sending to minimize number of ...
CommunityBot
- 1
1
vote
0
answers
35
views
Is it possible to get no solution from an optimal stopping problem
I recently read about the 37-percent rule as the solution to the secretary problem.
It says
To have the highest chance of getting the best applicant from a pool of applicants, you should interview ...
- 11
2
votes
2
answers
885
views
How should I learn from proofs in Applied Mathematics?
I am aware that similar questions have been asked here and elsewhere about how to learn from proofs. Some common advice is:
Most proofs are written in a polished form, not how they were first ...
- 455k
1
vote
0
answers
31
views
"Gaps in the Mats" problem
Problem Background*
The mat at your karate dojo composed of 160 square interlocking foam tiles. Along each edge of each tile, there are has five "teeth" (10cm long) and five spaces-for-teeth (again ...
- 846