Questions tagged [mathematical-programming]
Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.
33
questions with no upvoted or accepted answers
4
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0answers
108 views
Count number of pairs $(a,b)$ in an array such that $(a + b)$ divides $(a * b)$
We are given an array of size $N$ with integer entries $> 0$. We have to count the number of all such pairs $(a,b)$ with $a \leq b$ such that $a*b$ is divisible by $a + b$.
The obvious naive way ...
3
votes
0answers
92 views
Representing Computations on Transcendental Numbers
Consider the set of transcendental numbers that are not compressible to a finite base-2 representation. How can I compute multiples (more generally, any algebraic computation) of one of these numbers,...
3
votes
0answers
167 views
Drawing Zonotopes from an Adjacency Matrix
I'm conflicted whether to post this here or in either math.stackexchange or mathematica.stackexchange.
Define a "simple zonotope" to be a regular $2n$-gon which is tiled by the following rule: all ...
2
votes
0answers
54 views
Maximizing the product of a set of dot products
So suppose we have a set of vectors $X$ and we want to approximate the maximum of the following:
$\prod_{x \in X} b \cdot x$
where the components of $b$ sum to $1$
If it matters the components of ...
2
votes
0answers
133 views
Can cognitive architectures (CLARION, SOAR, ACT-R) be used for creative mathematical reasoning?
Can cognitive architectures (CLARION, SOAR, ACT-R, others) be used for creative mathematical reasoning? As far as I understand, then it is the best to encode formal mathematical knowledge in the ...
1
vote
0answers
31 views
Proof of Fundamental Lower Bound on Regret
Online Convex Optimization sees optimization as a continuous process in which the algorithm learns new aspects of the problem and improves upon.
Every iteration consists of the player making a ...
1
vote
0answers
18 views
Numerical integration of a function
For a particular physical system, the force is given by
$$F(r)=-\frac{d\Phi(r)}{dr}=\frac{r^5+2ar^3+a^2r-4a}{r^4(r^3+ar+2a)}$$
where $\Phi(r)$ is the potential energy which can be obtained as the ...
1
vote
0answers
28 views
How can I calculate the exponential integral?
(I'm not sure this is the right forum.)
I'm writing a program that uses the prime-counting function. Right now, I'm using x/log(x), but I want to switch to ...
1
vote
0answers
66 views
How to model the constraint of a circle placement problem mathematically?
I have a circle with radius $R$ and $N$ points on a 2D plane with known locations $(x_i,y_i), i=1,2,..N$. I want to place the circle such that it maximizes the number of covered points.
Let $d_i=(x_i-...
1
vote
0answers
66 views
Column Generation - Worst dual bound when adding various columns per iteration
I'm implementing a Column Generation algorithm. The pricing problem, in general, find more than one column with negative reduced costs(the master is a min problem). If i add only the most negative ...
1
vote
0answers
49 views
Program that solves mechanics diagram problems
There is a program, BEATRIX, that can understand textbook physics problems specified by a combination of English text and a diagram. The result of the understanding process is a unified internal model ...
1
vote
0answers
48 views
Fastest way to Add and Subtract multiple parts of a List
I am doing some research where I have a List containing numbers. For example
{5,10,98,22,13,15}
What is a fast algorithm to calculate all possible sums and ...
1
vote
0answers
85 views
RINS: start - incumbent and relaxation solution have all different values
RINS: Relaxation induced neighborhood search, firstly introduced by Danna et.al in 2004 in "Exploring relaxation induced neighborhoods to improve MIP solutions"
I wanted to design an example how the ...
1
vote
0answers
14 views
Symmetric Roles of the two problem solutions in RINS
Currently, I am reading the paper "Exploring relaxation induced neighborhood to improve MIP solutions" by Danna et.al. from 2004 and they are talking about a symmetric role of incumbent and the ...
1
vote
0answers
76 views
Research in realtime computational physics?
I am aware that there is a considerable amount of interest in computational mechanics for simulation of cloth, hair and other elastica, particularly for animation films. The methods developed by ...
1
vote
0answers
88 views
What is the Necessary math to understand books?
I have many problems understanding algorithms described in the books.
Well, I'm talking about the mathematical description of a problem.
For example: I don't understand how the math of Unscented ...
1
vote
0answers
35 views
Pedagogic reference on cut generating functions
Can you recommend an introduction to the topic of cut generating functions? I am looking for introductory or review-like material.
I did find the following survey paper, but it seems to be addressed ...
1
vote
0answers
62 views
Exponential maths operator
I have written a math library which handles really big numbers with good precision. Each digit is stored in a nibble and a 'nibble array' makes up the number. There is no epsilon portion, as for ...
0
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0answers
48 views
Algorithm Analysis - Binary Search Algorithm
The problem is from Data Structures and Algorithm Analysis Edition 3.2 (Java Version) Book from Clifford A. Shaffer. It is from the third chapter exercises, problem number 3.13.20.
Below is how it is ...
0
votes
1answer
28 views
Do all the numbers belong to same slot in the Hashtable?
I was reading the CLRS. In the Hashing Chapter on page 262 a statement says: "For example, if we know that the
keys are random real numbers $k$ independently and uniformly distributed in the range $0 \...
0
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0answers
32 views
Number of multiplications and additions in the given code
$N:=2^p$
Input: $f \in \mathbb C^N$
1: $n=N/2$
2: initialize vectors $f^{(1)}, f^{(2)} \in \mathbb C^n$
3: $w_N^0=1$
4: for $j=0,\ldots,n-1$ do
5: $\ \ \ \ \ f_j^{(1)}=f_j+f_{j+n}$
6: $\ \ \ \ ...
0
votes
0answers
22 views
Calculating the maxima of a function subject to a constraint
The first figure below shows the plots of a function $f(x)$ plotted for different values of a parameter $\lambda$, i.e., $f(x)=f(x,\lambda=\lambda_i);i=1,2,3,..;\lambda$ is maximum for the topmost ...
0
votes
1answer
59 views
Computer Vision Techniques to find Slope of beach in the 2D Images?
What I am planning to do is to calculate the height and estimate the slope of the segmented Object. The camera will be static and the Object of Interest is the slope of the beach.
I am finding harder ...
0
votes
0answers
17 views
How to identify a continuous shape and break it into minimum number of rectangles?
The input in this case is going to be coordinates in 2D of the vertices of the shape. There will be no curves, but the shape can have holes. The algorithm or program needs to identify the continuous ...
0
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0answers
28 views
How to calculate constraint check in BT of 4-Queens problem?
I have seen number of constraint check in paper of CSPs.
The constraint checking is counted as followed: when a value of a variable x is checked against a value of variable y, this is counted as ...
0
votes
0answers
33 views
Optimize an underdetermined system with quartic constraints
I encountered an optimization problem which does not belong to any well-known category of optimization.
The system has $M$ (typically $M=120$) real variables and $N$ (typically $N=100$) constraints (...
0
votes
0answers
41 views
How to generate evenly distributed random numbers from the tics of a Geiger Counter?
How can I generate random numbers from the tics of a Geiger Counter?
Say I have a file with the timestamps for every event.
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325
456
920
....
The time spans ...
0
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0answers
27 views
Algorithm for placing objects inside a square from outside to inside
I have a map that is 300x300 units. I have to place squares of 20x20 units inside that map from outside to inside. There are 3 different types of square, the space available inside the map needs to be ...
0
votes
1answer
62 views
0
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0answers
82 views
What is the time complexity of MATLAB's ode solvers?
Say I have a system that is $n$ differential equations that are all coupled together, over a time interval $[a,b]$ with timestep $t$. Is there a straightforward time complexity for MATLAB's built in ...
0
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0answers
27 views
Classify manifolds with neural networks
Can a neural network be used to find the genus of a 2-manifold given for instance as a CW complex?
0
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55 views
Math behind path tracing
I seem to remember seeing somewhere (many years ago) a writeup of the math behind calculating the outline of Metafont glyphs. The basic idea is you have a "pen" that is a circle or oval, that you ...
0
votes
0answers
468 views
Derivatives involved in Bilinear interpolation
If we choose a unit square in which the four points where the function $f$ is known are as shown in the diagram the interpolation formula for $f$ is:
\begin{equation}
\begin{split}
f(x+u, y+v)\approx (...
