Questions tagged [mathematical-programming]
Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.
34
questions with no upvoted or accepted answers
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112 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
148 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 ...
3
votes
0answers
114 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
170 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
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0answers
70 views
Counting triplets from three arrays satisfying the equation x^2 = yz
Let's say I have three arrays of positive integers X, Y and Z. You can assume that each of ...
2
votes
0answers
74 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 ...
1
vote
0answers
45 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
38 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
28 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?
1
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0answers
100 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
67 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
50 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
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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
87 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
79 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
94 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
36 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
63 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
50 views
Competitive programming: Good Subsets problem
An array of length K is called good if for each subarray of the array, the sum of the subarray is not divisible by K+1. You are given an array A of length N. Find the number of subsequences of length ...
0
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0answers
33 views
Optimal partitioning of n-arrays
You're given N integer arrays. Each array can have different size and contains unique values. However same integers can be found in different arrays.
The goal is to partition those arrays into K ...
0
votes
1answer
44 views
Is there a way to combine linear equation and inequalities into same equation in order to optimise software calculations?
I’m programming web application which has some tricky calculations and I would need some help with mathematical calculations.
What I'm trying to calculate:
I have number of items. Lets call items a1, ...
0
votes
0answers
14 views
How to cluster a dataset in which each data point is composed of a set of 2-dimensional coordinates
I have a dataset with totally $1000$ scenarios, each of which is composed of $5$ users' coordinates $(x_i,y_i), \forall i \in \{1,\dots,5\}$. Now, based on users' coordinates, I want to cluster these $...
0
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0answers
23 views
Stable matching with dynamic preference lists
I have a set $F$ of $n_1$ families, a set $C$ of $n_2$ children ($n_1<n_2$) and a set $M$ of feasible one-to-one matchings of the families with the children. All the children have the same ...
0
votes
1answer
62 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
34 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
1answer
119 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
70 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
52 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
69 views
0
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0answers
132 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
votes
0answers
56 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
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0answers
629 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 (...
-1
votes
1answer
19 views
Random numbers with condition in matlab
I need ’n’ random numbers that:
each one is bigger than ‘a’
their sum is smaller than ‘b’
How can I have that in Matlab?
