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 is mathematica not as popular as python? [closed]
Just want to know which is a proper learning platform for practicing math and statistics.
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What is the key difference between Mathematica and other logic computation program? [closed]
differences between Mathematica and MATLAB, Python, Java.
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Is the stochastic gradient descent minimization implemented in Mathematica?
I want to use Stochastic Gradient Descent method on its own (not for neural networks) to minimize an objective function in Mathematica. I couldn't find any SGD routine implemented in Mathematica (12.0)...
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Integro-differential equation with parameters
I am trying to solve an optimization problem with constraints that leads to the following integro-differential equation
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Finding element selected in NMaximize[{Min[...], constraints},{vars}]
How can I determine which element of Min[] is being selected in a NMaximize[{Min[...], constraints},{vars}] problem? For example,...
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How to play to Sound's sequences at the same time?
scaleHz[ff_, nr_] := Table[ff*2^(i/nr), {i, 0, nr}]
scale[fs_, d_] := Play[Sin[# 2 Pi t], {t, 0, d}] & /@ fs
ff = 440;
n1 = 12; n2 = 14; n3 = 16;
d1 = 1;
...
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Placing shapes along a square spiral
Proposed code example is inspired by the main idea of this challenge.
Wolfram Language provides great opportunities in computational geometry.
But not all of them are equal in terms of speed and ...
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Code not getting solved by NMaximize as 1/0 is encountred
I have the following code. This code requires to solve the model with two variables to optimize the function. a1 and a2 are the variables as shown in the code
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Code running for longer period to evaluate
0I have the following code where I want to maximize a stochastic function based on two variables. The code is taking a very long time to evaluate but still not giving answers. Can anyone help?
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Why, if you write the expression in the form of two functions, does the code stop working?
I would like to find the minimum of the function EER[a, v] using parallel computing.
If I write the code like this, it works:
...
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Understanding the calculation of the periodic function $f(x)=x-x^3, \quad -1<x<1$
It is given the following periodic function
$$f(x)=x-x^3, \quad -1<x<1$$
This is an odd function, so the coefficients $a_n,a_0$ of the Fourier Series are zero.
Usually, I face function with two ...
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Maximization of a concave function with contraints in the arguments
I have been struggling on solving this problem. Suppose you have a function f(x, y) that is concave in x and y. I want to find (x, y) that maximize f(x, y) with x ...
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Plotting a Stochastic function
I have a stochastic function and I tried to plot it in Mathematica
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Status of DualLinearProgramming
DualLinearProgramming is referenced in this tutorial
tutorial/ConstrainedOptimizationLinearProgramming
It exists in Mathematica ...
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Fitting parameter to match a dataset to another dataset
I am using a Module which calculates 3D-data based on 5 parameters and another input dataset.
I'd like to fit the result of this modul to another set of data.
Since my code became very long I will ...
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Can Mathematica resume the data that has been completely closed/quit?
Imagine that I run these four simple plots on a PC and then close and quit Mathematica, say the notebook file name is NOTE1
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What strategy would you adopt for this deep search on a function?
Ok, so I have a problem where I have a function that depends on 9 parameters and a bound condition
$$f(x,y,z,w,t,u,v,r,s)<K$$
Now all these variables take discrete values such as:
$$x \in \{x_1, ...
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How to more efficiently code integer constraints in LinearOptimization and Maximize
I've written the following code and it works, but my code syntax is inefficient. This is a linear optimization with binary (0,1) integer constraints. Instead of writing each Ri as between 0 and 1 and ...
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Maximization Problem
I am trying to find the solution of the following problem.
$ \max_{n_{\in [1,M]}} \frac{n \left(\frac{k (n-2 (\rho -1) \tau )}{\frac{k n (n-2 (\rho -1) \tau )}{2 (n+1)^2}+1}-2 \rho (\tau -1)\right)}{...
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How do to create 3D plot for the argument from two another arguments for maximum of the function?
How do to create 3D plot of ${t_{opt}} = {f_2}\left( {x,y} \right)$, where ${t_{opt}}$ is corresponding to maximum value of ${f_1}\left( {x,y,t} \right)$ at the limited ranges of $x,y,t$? If $t$ ...
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Routine to find all sets that are solution of a equation
So I have been wodering if Mathematica has any in-built function that would easily solve me these problem without manual search using for cycles that slow down the computation.
Let's imagine I have a ...
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Numerical Optimization over arrays of variable length
Consider the following command line. We work in the n=2 dimensions, in the sense that I have an 'x' variable of dimension n=2, and n+1=3 variables y1, y2, y3 of dimension 2 each. I have hard coded as ...
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Why doesn't FindInstance work with inequalities?
I'm trying to use FindInstance to find some simple counterexamples to the equality a^(1/n)+b^(1/n)=((a+b)^((1/n))) , with a, b and n integers. (Ex: a -> 9, b -&...
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How to provide an RNN various type of inputs?
I'm trying to build an RNN in Mathematica.
My window is only 2 but the variables are of different types:
...
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Can I solve a system for a postive semidefinite variables?
I have the following system, where I want to find the solution set consisting of real, nonzero, symmetric positive semidefinite matrices $G$ and $DD$ such that the block matrix $X$ defined below is ...
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Finding minimum of a symbolic function [closed]
Why does Mathematica fails to find the minima of the two variable function with real coefficients. The function and my attempt is given below.
Input:
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NMinimize does not reach the minimum
I need to minimize numerically an expression with constraints. The expression also includes a numerical integral (called 'PNoninteract').
The minimization apparently stops prematurely (I know roughly ...
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Constrained total of rowwise maxima of a matrix
Suppose we have a matrix defined as follows:
$$x=\begin{bmatrix}
9 & 8 & 1\\
8 & 5 & 1\\
1 & 1 & 8\\
\end{bmatrix}$$
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Convergence with Maximize - Iterations, Precision
I have problems with some applications for finding convergence - below is one example of failure for {x=0.35,y=0.35,z=0.3}, but it works fine for {x=0.3,y=0.3,z=0.4}.
How can I increase the iterations ...
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Numerically determining the minimum/maximum distance between two ellipses
The smaller ellipse is contained within the larger one.
By 'minimum distance', I mean the distance that minimises;
Sqrt[(y1 - y2)^2 + (x1 - x2)^2]
By maximum, I ...
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Nminimize output of ParametricNDSolveValue
I want to minimize the time a family of ODEs vanishes.
To do so, I'm using WhenEvent to extract the vanishing time and put the result inside Nminimize:
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Solving an equation involving exponential function
I have an equation
$$ c \tan \left(\theta_{\mathrm{OPT}}\right)+\frac{a b A \exp \left(-b\left[\theta_{\mathrm{OPT}}-a\right]\right)}{\left[a \exp \left(-b\left[\theta_{\mathrm{OPT}}-a\right]\right)+1\...
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LinearOptimization and Accuracy
Surprised to encounter the following issue in handling Accuracy with LinearOptimization:
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Mathematica does not show anything after running for higher iterations
Consider a BVP: $y^{\prime\prime}=\frac{3}{2}y(t)^{2}$ with the boundary conditions $y(0)=4$ and $y(1)=1$. The exact solution is $y(t)=\frac{4}{(1+t)^{2}}$ and the initial guess is $y(t)=4-3t$. Now I ...
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Creating Table/LaTeX with Extreme Points based on parameter values in a table
I would like to simulate extreme points and illustrate results with exogenous parameters and optimal values. I created the input table and table with the optimization problem for a simplified example.
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Minimizing a function over a bounded domain with binary variables
I want to minimize the following function:
$$
f(m,n)= \sum_{i=1}^N\Big\{ \alpha_i(x_i-m)^T(x_i-m) \Big\} + \sum_{i=1}^N\Big\{\beta_i (x_i-n)^T(x_i-n) \Big\}
$$
where $m,n$ are all 2-d vectors:
$$
m:= ...
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In NMinimize, how to incorporate constraints on positive semidefiniteness of a matrix which is not the matrix variable being optimised?
The problem
I want to solve the following problem for symmetric matrix $X$:
$$
\begin{aligned}
\min_{X\succ 0} \; & -\log(\det(X)) & \\ \text{subject to} \; & \begin{pmatrix} X &...
CommunityBot
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Optimize the path length in a KaryTree
I have a engineering problem that I found suitable in formulating it in graphs. A source node supplies pressure or whatever. Each node (vertex) has two edges of a certain e.g. pressure loss...whatever....
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Equality contraint violated with NMinimize
I am attempting to numerically optimize a function of only 2 parameters k, θ. There are two inequality constraints (1 each on k ...
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Evaluation stops without output or error when using Nested Maximize
I am trying to evaluate a max max min problem. The code is as follows:
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LinearOptimization thinks 0-1 ILP is an MLP
I try to solve this 0-1 integer linear program (maximize, thus the minus) with LinearOptimization:
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NMinimize keeps returning Indeterminate for well defined function
I am attempting to numerically optimize a function of only 2 parameters k, \[Theta].
The function is well-defined and the constraints are simple. However, the ...
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Why is the plot of low quality produced?
Stydying the modulus of continuity of $\sqrt x \log(x)$ in version 13.1
on Windows 10, I execute
...
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Memory problem for maximizing a multivariable function
I need to maximize the following function. Unfortunately I have to maximize without using numerical methods to prove that the maximal value is 3Sqrt(2Sqrt(3)-3) (about 2.04375). I tried it twice (once ...
CommunityBot
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Interior point method for unconstrained problems
I was recently working on applying the FindMinimum function to $f(x)=(x+1)(x-1)$, and chose the interior point method as the 'method', which yielded $x=0$. I would like to better understand how the ...
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Maximize and NMaximize in comparison
If on one hand:
N@Maximize[{Sqrt[y^2 - x^2], x + y^2 == 0 && 0 < y < 2 && -y < x < y}, {x, y}]
{0.5, {x -> -0.5, y -> 0.707107}}
...
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How to solve this optimization problem?
Is there an effective method to solve the following optimization problem in Mathematica?
\begin{align*}
\min & \quad -t \\
\mathrm{s.t.} &\quad A \succeq 0,\,a=1
\end{align*}
I mean A is ...
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