Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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How to do edge detection in Mathematica?
I have some pictures of water level and I want to do edge detection, I used the following command, but this command is vertical edge detection and I want horizontal edge detection and water level. ...
- 159
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How to make a density plot for an isotropic function written in cylindrical coordinates?
$f(\rho,z)=2\rho^2+\frac{2}{3}z^2 \quad$ is a function in the cylindrical coordinate system $(\rho,\theta,z)$
The function $f(\rho,z)$ is isotropic because it does not depend on the angle $\theta$. ...
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Using UnrankPermutation with Maximize
I want to try and use Maximize with UnrankPermutation to find Costas Arrays (or as close as possible) for a given length l with first two elements l, 1. A permutation array that maximizes the number ...
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NMinimize or other means for mixed-integer problem with constrains
Given two real numbers 0 < x < 1/2, 0 < y < 1/2 and an integer n, harmonics are ...
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Improve performance of Linear Optimization
EDIT
I am reframing the question here by pulling out the relevant part about linear optimization, you can find the original question and the entire code down below.
I am trying to increase the ...
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Find knee by intersecting line method
I have an x-y data list. The data is here. It looks like below:
I want to mark the knee location. I mean I need to find the point of greatest slope change and get the x coordinate of this point. ...
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What is the network structure of Ademxapp Model A1 Trained on Cityscapes Data in the Mathematica?
I want to implement the model (Ademxapp Model A1 Trained on Cityscapes Data) on my data for segmentation, so I need the partial structure of this model, can anyone help?
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Maximize does not finish or does not work
I need to maximize the following expression over the two variables $d$ and $a$, in terms of the parameters $t, m, k$:
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Trying to use Linear Optimization to solve inequalities
I am trying to use Mathematica to get bounds on some quantities using a certain procedure which is called conformal bootstrap. For the users who don't come with a background in HEP, I am basically ...
- 185
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NMinimze cant find points that satisfy constraints
NMinimize cant find solutions for a function which clearly has one. Setting a working precision resulted in some output, however with error messages about tolerance and precision.
Heres my code. The ...
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Numerical Error using compile
I'm trying to compile a function and I'm running into the following error
CompiledFunction::cfne : Numerical error encountered; proceeding with uncompiled evaluation.
I think I have succeeded in ...
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Minimax problem where a combination of Minimize and Maximize gives no result at all
I rarely use Mathematica, but I usually do not have any problem with simple commands like Minimize or Maximize. I have find to ...
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Finding maximum value of a function with parameter
How can I find the maximum value (and the corresponding $x$) of the following function with parameter $t$:
$$ f(x) = |x^2-tx + 2t|$$
on a closed interval $x\in[0,1]$?
I tried using ...
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Finding the Minimum of a Four-Variable Function
Greetings esteemed colleagues. I had previously posted regarding the minimisation of a function using Mathematica, and colleagues were kind enough to provide some useful suggestions that proved quite ...
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Help with code for impulsive optimal control problem
I am using Mathematica 13.3 to numerically solve/generate numerical plots for my impulsive control problem.
The optimal control problem is:
T is time from0 to T where T is the terminal time
K(t), B(t) ...
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Finding the symbolic root of a non-linear function with fractional exponents
Define $f(x, a, t) = (x-t)^a - \frac{x^2}{2}$ where $x>0$ is the main variable of interest and $\alpha \in (0,1)$ is the parameter of curvature:
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Finding the maximum of a non-linear function symbolically
I have the function $$f(x,\alpha) = x^\alpha - \frac{x^2}{2}$$ where $x>0$ is the main variable of interest and $\alpha \in (0,1)$ is the parameter of curvature:
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Optimization problem with complex and real values
I have the following optimization problem:
$\underset{{{a}_{1}},...,{{a}_{m}}}{\mathop{\max }}\,\parallel \sum\limits_{n=1}^{N}{{{a}_{n}}}{{\varpi }_{n}}{{e}^{j{{\theta }_{n}}}}{{\varphi }_{n}}{{\...
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Calculate Fourier coefficients in optimization problem [closed]
I am using Differential Evolution optimization algorithm to estimate Fourier Coefficients to recover my objective function. In this case, coefficient samples are generated, and then the algorithm ...
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Fitting a free parameter by matching a an array with another array
I have the following problem that I can't figure out how to solve.
I have two measured signals, (data1 and data1), and their measured sum (datasummeasured). I have a theoretical description of how the ...
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Is it possible to ask Mathematica to obtain the function describing the upper and lower boundaries of a combinations of functions?
Assume that I have three one-variable non-periodic functions $f(x),g(x),h(x)$ for $x>0$. The question is: is it possible to ask Mathematica to obtain the function describing the upper and lower ...
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Why can't we find the minimum value of 2a+b?
Find the minimum value of 2a+b
In[27]:= Clear["Global`*"]
f[x_] = Abs[Log[x]]
Minimize[{2 a + b, f[a] == f[b], a > 0, b > 0, b > a}, {a, b}]
No ...
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How to use Semidefinite Optimization for a problem?
What is this error message and how can I make this SemidefiniteOptimization work?
Also, is there an easier way to input my constraint in terms of each element ...
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Efficient use of GatherBy on large list to remove duplicates
I have a large nested list of rules, wherein elements which have repeated entries on the LHS of the rules should be deleted. For instance
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How to find the eigenvalues of a particle in the Coulomb field using NDEigensystem?
As advised in the previous two questions (Why, if I enter an angle into the function, then does the code not work correctly?, let us solve the problem for the Coulomb potential in spherical ...
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NMinimize and NMaximize stopping evaluating for more complex conditions
I am trying to obtain the maximum and the minimum of (the negative of) a function F(R,P) given by
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How to approximate an exponential series?
Consider the following expression
$$
y_j= \sum_{k=0}^{L} \frac{e^{-\sum_{i=-k}^k(k-|i|)x_{j+i}}-e^{-\sum_{i=-k}^k(k+1-|i|)x_{j+i}}}{\sum_{i=-k}^k x_{j+i}}\tag{1}
$$
for $1\leq j \leq L$. Given smooth ...
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Eigenvalues and eigenfunctions of a parameter dependent system
There is the following system $H=-\frac{1}{2}\Delta-a\frac{1}{r}$, where a is a parameter. I'd like to find eigenvalues and eigenfunctions depending on the ...
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How can NDSolveValue and ParametricNDSolveValue be used correctly to find eigenvalues and eigenfunctions?
NDEigensystem can be used to find the eigenvalues and eigenfunctions of the following system $H=-\frac{1}{2}\Delta-\frac{1}{r}$.
...
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How to run QR decomposition inside NMinimize function?
I'm trying to optimize a custom function using NMinimize in Mathematica. The custom function contains QRDecomposition in it ...
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NMaximize error: The function is value....is not a number
I cannot manage to solve this problem:
$$max_{p1,p2} \hspace{0.1cm} (p1 - w1) * \frac{\exp(beta*x1 - alpha*p1)}{1 + \exp(beta*x1 - alpha*p1) + exp(beta*x2 - alpha*p2)}$$
$$ + (p2 - w2) * \frac{exp(...
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Solving a system of complex matrix equation using Reduce function
I am trying to solve a system of four matrix equations using Reduce function. The system arises in Quantum Information. The system is solvable with a solution i.e. phi, but the following code gives ...
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Find minimum of integral with two variable terms
I wanted to see an approach to solving this problem with Mathematica: https://math.stackexchange.com/questions/4723531/how-would-you-attack-this-problem
Determine real numbers a and b so that the ...
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ArgMax returns the input
I am new to Mathematica so I don't know if I am missing something.
I am trying to use ArgMax for a specific function I have, which includes ...
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SVD decomposition with optimization
Let's suppose there is a matrix A nxn, which will be decomposed into SVD:
where ui and vi are singular vectors composing matrix U and V. sigma is a vector that contains the eigenvalues. In ...
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How should a function written through the Module be written in the FindMinimum correctly?
There is a function that is written using a module ...
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Parameter Estimation on ODE Using NMinimize (Least Squares Method)
I'm trying to estimate the parameters in this equation using this code:
...
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What is the correct way to use FindMinimum with NDEigensystem?
I would like to find the minimum of a function dE[me_, mh_, e0_] using FindMinimum but Mathematica shows errors from ...
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Optimize parameters for differential equations
I have differential equations f11, f12, f21, and f22 with respect to t with parameters A and B. I've defined and solved these equations using NDSolve in Mathematica as follows:
...
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Why mathematica Minimize function cannot handle Integers constraint in this case?
I am an electrical engineer and sudenly a problem of this form appear during my research
For this kind of problem, Mathematica can work just fine. But as soon as I as the Integers option then I ...
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Finding the dimensions of the cylinder that can cover $n$ given smaller cylinders (based on empty space, not least materials)
Let $r_k$ and $h_k$ be, respectively, the radius and the height of the $k^\text{th}$ cylinder. We have $n$ cylinders.
Let $R$ and $H$ be, respectively, the radius and the height of the big that can ...
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Minimize is returning unevaluated for a simple positive integer domain problem [closed]
I don't understand why the following Minimize code is returning unevaluated. I believe I have it coded properly and the expected minimum is $x=14$ and $y=1$.
<...
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Finding the sum of eigenvalues of a matrix depending on the parameters
There is a system that has the following Hamiltonian: $H=-\frac{1}{2}\Delta-\frac{1}{r}+\frac{B^2}{8}\rho^2-\frac{B}{2} (m + 2 m_s)$, where $r=(\rho,z,\phi), B=5, m=0, m_s=-1/2$. To find the ...
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How can I find the minimum value of an algebraic expression as a function of some parameters?
Minimize[
{
(2 a (a^2 - c^2))/(a^2 - c^2 Cos[θ]^2),
0 <= θ < π, a > 0, c > 0, a > c
}, {a, c, θ}
] // FullSimplify
The expected result ...
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FindMaximum is not working properly?
I'm trying to find maximum of the functions that I created by interpolating experimental data by using FindMaximum:
...
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How to estimate whether the objective expression has a global minimum value?
I have an expression concerning $x$ as follows (from my friend).
$f(x)=x^4-2 a d x^3-2 b d x^3-2 c d x^3-2 d x^3+a^2 d^2 x^2+b^2 d^2 x^2+c^2 d^2 x^2+4 a d^2 x^2+2 a b d^2 x^2+3 b d^2 x^2+2 a c d^2 x^2+...
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Is FindShortestTour really exact? [closed]
I have read online that the FindShortestTour function on Mathematica uses the Concorde TSP solver, which is meant to provide exact solutions. However, I have been playing with this problem on my own, ...
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How do we optimize the lowest eigenvalue of a symmetric matrix using NMinimize?
I am trying to diagonalize the symmetric matrix while optimizing
the lowest eigenvalue subject to constraints.
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