Questions tagged [mathematical-programming]

Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.

36 questions with no upvoted or accepted answers
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109 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 ...
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2answers
107 views

Usefulness of Differential Geometry

I recently came across these books: Differential Geometry and Lie Groups: A Computational Perspective Differential Geometry and Lie Groups: A Second Course Their subject matter really intrigues me, ...
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0answers
146 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
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0answers
111 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,...
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168 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 ...
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63 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
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0answers
67 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 ...
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41 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 ...
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0answers
19 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 ...
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31 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 ...
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0answers
91 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-...
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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 ...
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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 ...
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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 ...
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86 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 ...
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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 ...
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78 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 ...
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91 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 ...
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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 ...
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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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1answer
34 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, ...
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0answers
11 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 $...
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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 ...
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53 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
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1answer
50 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 \...
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33 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: $\ \ \ \ ...
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23 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
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1answer
104 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 ...
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59 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 (...
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41 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 ...
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114 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 ...
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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?
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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 ...
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592 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 (...
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25 views

mathematical formulation complexity

How to find the complexity of a mathematical formulation ( in terms of constraints and variables) (We refer generally to the notation (o(n^2) variables and o(n^3) constraints) ( I would be grateful if ...