# Questions tagged [mathematical-programming]

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

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### 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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### 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 ...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Find a subsequence with fastest time for specific distance

I have two arrays. ...
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### 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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### 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 ...
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{split} f(x+u, y+v)\approx (...