# Questions tagged [mathematical-optimization]

Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.

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### Why hasn't the minimum value of a+b been determined?

Why hasn't the minimum value of a+b been determined? Minimize[{a + b, 9 == 9^(1/a) 3^(4/b), a b > 0}, {a, b}] Find the minimum value of a+b. The limiting ...
121 views

### Modifying FindMinimum to work for noisy functions?

I have an eigenvalue problem where I'm minimizing a function which is a bit noisy. FindMinimum seems to fail to work in this setting, can anyone see an alternative ...
124 views

### How to speed up optimization?

Finding a quadratic polynomial of the best approximation in $L$-metrics to $\sin(x)$ on $[0,5]$, I execute ...
50 views

### How to find the minimum value of multiple function in the chi-square distribution?

I got a multiple function in the following way： ...
59 views

### How to speed up maximization of the Solve output?

I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains. Here is the code ...
1 vote
118 views

### Could a minimization problem be easily converted into a NonlinearModelFit?

I am trying to fit data that is correlated, such that the $\chi^2 = (f(x_i,pars)-y_i)(Cov^{-1})_{ij}(f(x_j,pars)-y_j)$. However, NonlinearModelFit only accepts ...
1 vote
62 views

### Find an instance satisfying equation

I have the following equation with two variables xi and nu. ...
26 views

### NMaximize simple function

I am trying to solve a maximisation using Mathematica. The objective function, though involved, can be broken down into many simpler terms. One of these terms is ...
60 views

### Normalizing a plot by introducing a variable

I am trying to plot the graph between P and x. My teacher wants me to normalize this graph by introducing a constant $k$ to get $P/k^2$ on the y-axis and $xk$ on the x-axis. I did that by doing a ...
36 views

### NonlinearModelFit with NMinimize Submethods and Selective or Mixed-Head Constraints

Problem: I believe I've found a two related bugs associated with using NonlinearModelFit while making a Method call to NMinimize's submethods, e.g. "RandomSearch" and "...
78 views

### Finding the maximum of a function [closed]

I can’t find the maximum of the function, although the graph shows that it exists. Maximaze and FindMaximum give different results. However, these results do not coincide with the graph. ...
144 views

### Numerical Galerkin method with parametrized interpolation function

modified Here I try to realize a numerical fit (Galerkin method) using parametrized Interpolation function to fit examplary Exp[x] in a given grid. So far I tried <...
2k views

### Efficiently Mowing Grass with Mathematica

Recently, I was mowing my yard and was thinking about how to use the least amount of time/fuel and how to simulate. Mowing a yard that is shaped as a convex polygon is not difficult, you can just make ...
1 vote
79 views

### Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
43 views

### FindMinimum with many Sums and NIntegrates is very slow

I want to calculate the global minimum of an equation which has several hundred Sums (I used 300 in this code), but the calculation is very slow. My code is as ...
1 vote
83 views

### How to calculate maximum between two or more lists element by element and also the index corresponding to the maximum element?

I am looking for a function say f such that for example f[{a1,b1,c1},{a2,b2,c2}] will give {Max[a1,a2],Max[b1,b2],Max[c1,c2]} and also a function g say such that g[{{a1, a2, a3}, {b1, b2, b3}},{{c1, ...
97 views

### How to optimize the sum of squared values?

How can we optimize the sum of squared values (or the sum of multiple absolute values)? I found that using ArgMin is very slow. Are there any other methods to accelerate the solution? Edit：I am ...
1 vote
85 views

### Nearest inside Minimize

How to use Nearest inside Minimize? The following returns errors but if # - {a, b} is ...
164 views

### Problem with FindGeometricTransform and NMinimize

I'm interested in Centroidal Voronoi tessellation. Here are two examples of unit disk tessellations: They are the same with respect to rotation. Recently, I've found ...
1 vote
253 views

### How to interpolate an implicit function?

chi(t) is implicit function. The implicit function can be plotted by ContourPlot. Is it possible to obtain chi(t) explicitly using function interpolation? ...
91 views

### Why doesn't NMinimize work with NSolve?

Why does NMinimize throw the error and how to fix it? ...
255 views

### Packing unequal spheres into minimal cuboid

There are several non-overlapping spheres in 3D. How to find a cuboid Cuboid[{a,b,c}] containing these spheres with minimal ...
114 views

### Problem with Min and Max [closed]

s=min{max{0,a}, max{0,b}, 1/(1-a) max{0,1-a}} is there any alternative way to make this more concise without condition and in one expression. Condition is -infty<a<infty and -infty<b<1
281 views

### How to solve this equation over the integers with Mathematica?

I try to solve with Mathematica 13.3.1 on Windows 10 the problem $$x^2+2^{x^2+1990}-y^2=2^{y^2+y}+y-1990\land x+y>1990,\, x\in \mathbb{Z},\,y\in \mathbb{Z}$$ which originates from Bauman Moscow ...
1 vote
135 views

### How to calculate the depth of the lake in mathematica?

I want to calculate mean depth of Goose lake (mean depth=4.6 m), I use bellow command for this operation, But this command is not automatic and we have to create the coordinates manually, and on the ...
101 views

### Why can't NSolve find values that FindInstance can?

I am trying to solve for \[Epsilon], given three input paramters n, x and ...
1 vote
118 views

### Find the point with the largest slope change

I have a list of x-y data: ...
1 vote
57 views

### FindMinimum can't evaluate Nearest numerically

I'm trying to use Nearest as a function to minimize over: a toy example is ...
192 views

### Finding a fixed point of function without a closed-form solution

I am trying to find a fixed point of a function that does not have a closed-form solution (it is the solution to a NMaximize problem). The following simplified problem, which would have an easy ...
121 views

### How to estimate Lake area and volume in Mathematica?

I have a satellite image of the lake and I want to estimate its area and volume. Actual volume:1.49*10e8 m^3 Actual Area:36.9 km^2 I did the following command to find the volume, but it is not very ...
59 views

### How to extract shape from image in the Mathematica?

I have some satellite images for the lakes. How to extract the shape of the lake with maximum accuracy from the image?
37 views

### I am trying to plot the function below, however, it does not seem to be working [closed]

Do you know what I am doing wrong? The image I put below shows the function I would like to plot.
94 views

### Using GraphicsGrid for density plots with color scales

I would like to arrange the density plots in a certain order using GraphicsGrid. But when using GraphicsGrid, there is problem with the color scale, it doesn't display completely. How should ...
1 vote
77 views

### What are some ways to speed up calculations

Below is the code for calculating the eigenfunctions and eigenvalues of the following system: \$HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
1 vote
253 views

### How to find a densest configuration of several non-overlapping unit disks? [closed]

Let us consider three non-overlapping unit disks in the plane. I'd like to find a configuration of these disks s.t. the area of the convex hull of these disks is smallest. This is related to the ...