Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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Let R be the region enclosed by the curves [closed]
Use Mathematica. Let R be the region enclosed by the curves y=x^3-3x and y=2x^2
(i) Sketch the region R.
(ii) Find the area of region R.
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draw a triangle [closed]
Given a triangle with vertices (0,6), (4,0), and (6,8). How do you use Graphics to draw the triangle as well as it's altitudes, perpendicular bisector, medians, and angle bisectors in Mathematica?
3
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NMinimize NelderMead postprocessing method [closed]
I am using NMinimize with the NelderMead method. I have a very good initial solution supplied via InitialPoints. If I turn off postprocessing ("PostProcess"->False) then the output is ...
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Why do the solutions from the FindMinimum produce a lot of unphysical oscillatory points?
The parameters. Here I mention all the parameters I use in my code including some of the functions that I define for convenience
Parameter set-I
...
2
votes
1
answer
28
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Using NMinimize for a real-valued function of complex variables
I am trying to use NMinimize to minimize a real-valued function of complex arguments, with a supplied initial point. This doesn't seem to work well. For example, the following gives errors like "...
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1
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Finding only non-negative roots with FindRoot
Given an arbitrary function F, how do I force FindRoot to look only for non-negative roots, returning nothing otherwise?
- 4,362
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30
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Calculating minimal unknown coefficients of a sum
I have a problem, where I have to find the minimum of a function with a sum in it (coefficients are unknown):
psi[x_] := 1 + a*x + b*x^2 + c*x^3 + d*x^4 + ...
...
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15
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3
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Performing Tobit Regression in Mathematica by Maximum LogLikelihood
I am trying to estimate a tobit model by maximum likelihood method in Mathematica. I can not find the build-in function. So I try to perform it manually.
Here is the log likelihood function of Tobit ...
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Invalid Constraints error in Non-linear Optimization
I am trying to write the code to solve a certain optimal control problem, but I keep running into an issue when I pass on my constraints to NMininimize[].
The ...
1
vote
1
answer
61
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Simple SDP using Hermitian matrices
I would like to run the following semidefinite program
$$ \textrm{Minimize}\,\, \textrm{tr}\big({AX}\big)\\
\textrm{subject to}\,\, X \geq B_1\,, X \geq B_2\,, $$
where $A$, $B_1$ and $B_2$ are ...
0
votes
1
answer
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Find the minimum value of a constrained multivariable function [closed]
Say I have a function of four variables $f(x_1,x_2,x_3,x_4)$ and a constraint $g(x_1,x_2,x_3,x_4)$ (both are quite complicated, that's why I don't write them explicitly). I want to find the minimum ...
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Moving average MA(1) coefficient estimation
I am new to mathematica, I have some simulated a moving average, MA(1), data and I want to estimate the coefficients, theta, of it using Maximum likelihood estimation or log likelihood. Can someone ...
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Is there a way to print all the outputs NMaximize runs through for different variable combinations?
I've got some function of 4 angles ($\theta1$, $\phi1$, $\theta2$,$\phi2$) that I'd like to maximize using NMaximize, but I'd like to be able to see the output for ...
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2
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1
answer
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Using the result of Solve as a function of parameters
I am trying to find b2 maximising a function I named 'EG1EUB'. And 'EG1EUBb2' is the frist order condition. Based on my understanding, Solve gave me a single solution saying that b2 is the second root....
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Reduce local maximum of function, a problem of optimization
So I have this almost linear function (for evey frequency it is the square root of a sum of squares), but not quite.
...
3
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1
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Holes in ContourPlot3D
I have a polynomial polyHP and I put some conditions Reg on it and I try to plot it with ...
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Fast pairwise difference
I'm trying to construct a matrix $A_{ij}=X_i-Y_j$ where $X$ and $Y$ are vectors with thousands of real numbers. The fastest and closest thing I found is ...
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Can I avoid FindMinimum ruining my Asserts with symbolic stuff?
I am new with Mathematica, so forgive me if I completely misunderstood the nature of the problem...
Problem description
I want to optimize a fairly complex function bypassing explicit derivative ...
- 151
2
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2
answers
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NMaxValue - function is not a real number
I'm trying to use NMaxValue to numerically find maximal values of the function F[z]. The problematic part of my code is as ...
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Numerical solution of the integral for the profile of a vortex
I am trying to solve numerically the integral extracted from the article by Vanyó et al. (https://doi.org/10.1103/PhysRevE.90.013002)
$$
h(r') = \int_{0}^{r^{\prime}} \frac{\partial p}{\partial r} / \...
2
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2
answers
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Getting an exact value from FindMinimum [closed]
FindMinimum[{(Sin[a]^2 + Sin[b]^2)/Sin[c]^2,
a + 2 b == π/2 && a + b + c == π && a > 0 && b > 0}, {a, b,
c}]
The numerical ...
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Computing $c$ that minimizes $\left(\sum_i h_i c_i\right)^2/\sum_i h_i^2 c_i$
I need to solve the following problem. Given a set a vector of positive numbers $h_i$, find $c_i$ which solves the following optimization problem :
minimize
$$k$$
subject to
$$\begin{equation}
k\sum_i ...
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Is it normal that adding constraints on the parameters of NonlinearModelFit increases execution time 100 times??
Normally, reducing the optimization domain by adding constraints should reduce the time of execution. In my case however, this puts the NonlinearModelFit in a coma. Without constraints, 8 seconds ...
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Maximizing functions with statements similar but result different
I would like to know why when I maximize the sum of two functions with similar expressions (Qu and Qm), it gives me different results (nu and nm), since they should be the same results because the ...
0
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1
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Verbose NMaximize for long optimisations
I am currently running a command: NMaximize[{expression, constraints}, {x1, ..., xn}] that takes quite a while to converge. Is there a way to run Nmaximize in a ...
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Solving the Unbalanced Assignment Problem with FindMinimumCostFlow?
I want to adapt this code from this answer to work with unbalanced bipartite graphs:
...
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0
answers
33
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How to define a multivariate region of space on which to minimize a function?
My objective is to optimize a function that takes two vectors as argument: a parameter vector of probability to be optimized on, and the input data.
In other words am trying to tell Mathematica that ...
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46
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0
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1
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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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49
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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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1
answer
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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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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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vote
1
answer
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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 ...
2
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answers
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2
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1
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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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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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1
answer
103
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0
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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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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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2
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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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2
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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 ...
2
votes
1
answer
69
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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 ...
3
votes
1
answer
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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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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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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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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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1
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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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1
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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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