Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
1,721
questions
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1answer
48 views
Maximization under constraints / find maxima
I am trying to code the following maximization program that I am not able to solve algebraically (Of course I manage to get the first derivative, but struggle finding its root):
$\begin{equation} Max_{...
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0answers
66 views
Approximate integer factorization
Suppose we would like to compute an approximate prime factorization of a large integer x in the sense that the difference between ...
7
votes
1answer
108 views
Kronecker Square Roots
I'm interested in computing the 'Kronecker Square Root' $\mathbf{A}_{n\times n}$ of a matrix $\mathbf{M}_{n^2\times n^2}=\mathbf{A}\otimes\mathbf{A}$. In case it doesn't exist, I'd like to find the ...
0
votes
1answer
45 views
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:
$$
m:= ...
1
vote
1answer
63 views
Maximization of piecewise function
I'm trying to maximize piecewise functions with parameters but haven't been able to do so. Here is a minimum example:
...
0
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0answers
21 views
General::munfl - Precision lost in LinearModelFit
I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3)
...
0
votes
2answers
69 views
NMinimize over a list of integers
I'd like to minimize some function (of 3-4 variables) over a big list of integers, but not consecutive. Like arr = {5, 10, 7, 101,...}
I did not understand this ...
0
votes
1answer
37 views
Trouble using NMinimize [closed]
I am trying to minimize five function at the same time. I am running in some trouble minimizing this function, as since I am not that familiar with Mathematica I really do not know what I am doing ...
0
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0answers
39 views
Low Tolerance making wrong behavior of LinearProgramming?
I was working on a code that needs to check feasibility of LP problems. I visited Checking linear program feasibility? and used the code. With this code, since there is 1 at the last position at every ...
0
votes
2answers
102 views
How to solve a nonlinear system of equations with exponential terms
I want to solve this parametric nonlinear system of equations in Mathematica:
$$x−1−(e^{a−x}+e^{b−y})/(c+e^{b−y})=0$$
$$y−1−(e^{b−y})/(c+e^{a−x})=0$$
and I used this code:
...
2
votes
1answer
46 views
Stop Minimization after condition
I want to interrupt the optimization of a function when a particular condition is satisfied. Here I provide a test function.
...
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2answers
131 views
Is there a way to do this more efficiently?
I'm trying to write this Mathematica function to find the optimal price for a model, given some model parameters. This is a stylized example of what I'm trying to do, and I'm wondering what's a better ...
0
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1answer
79 views
What has Maximize been thinking about for so long?
The command
Maximize[{Sqrt[2 x + 13] + (3 y + 5)^(1/3) + (8 z + 12)^(1/4), x + y + z == 3&&{x,y,z} >= 0}, {x, y, z}]
is running without any response on ...
0
votes
1answer
23 views
NMaximize giving error when trying to find global maximum [closed]
I've been trying to use mathematica to find the maximum of 1/(1 + e^(-(x - 9))) + 1/(1 + e^(-(y - 9)) where x>0,y>0 and x+y=100.
This is the code I've been using:
...
0
votes
1answer
49 views
How to force NMinimize to find the correct global minimum for equation with many local minima?
I have a function that I am unable to recover a solution for. Here, 0.533... and 0.428... are the exact solutions for Rs[399] and ...
0
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0answers
19 views
NArgMin “function value is not a number” error
The "function value is not a number" type error seems fairly common. Forgive me, but I can't seem to fix my issue using some of the other posts on this site.
I'm working on a problem where I ...
0
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0answers
28 views
Evaluating function of two variables inside NMinimize with respect to second argument
Consider three functions:
f[t_, 1] := {Cos[t], 1, 0}
f[t_, 2] := {Sin[2 t], 1, 0}
f[t_, 3] := {Cos[t - 2], 1, 0}
For each $k=1,2,3$, let $g(\cdot,k)$ be the ...
0
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1answer
75 views
How to derive all KKT points of a parametric optimization problem
Suppose we have a symbolic optimization problem where all parameters and decision variables are nonnegative like the following problem. I would be thankful to know if there is any method to find all (...
0
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0answers
59 views
Calculating my code for higher values of `k`?
How do I calculate the mean of A for higher values of k
...
7
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3answers
359 views
Speed up minimization of a high-degree polynomial
For fixed $s$ and $n$, I need to find $\alpha$ which minimizes the following expression
$$h (I-2\alpha H + 2\alpha^2 H + \alpha^2 \mathcal{H})^s x0$$
where
$$
\begin{array}{lll}
h&=&(1,\frac{1}...
0
votes
2answers
173 views
Is it possible to calculate the desired area analytically?
I have the three two-variable curves $f,g,h$ with $0\leq x\leq \frac {\pi}{2} $ and $0 \leq y \leq \pi$
I use ContourPlot as
...
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0answers
30 views
Why do I get the (NMinimize::nrnum) error and how to fix it?
I have an energy function which depends on the angles of the electrons({x} symbol for theta) and phase of electrons({y} symbol for phi). I am using NMinimize to minimize the energy with respect to {x}...
4
votes
1answer
126 views
MaxCut SDP primal in mathematica
How could one formulate the primal SDP for MaxCut in Mathematica.
I am aware of this tutorial using the dual:
https://www.wolfram.com/language/12/convex-optimization/max-cut-problem.html?product=...
5
votes
4answers
147 views
Are there any alternatives for NIntegrate to calculate the area for which $f(x,y)<0$?
I have this two-variable function
$$f(x,y)= (8 \cos (x+y)+7)\cos \left(\frac{x}{2}\right)+\cos \frac{x-2 y}{2}+2 \cos \left(\frac{3 x}{2}\right) $$
where $0<x,y<\pi$. I want to calculate ...
0
votes
1answer
51 views
Integral with exponential function
Could you please help me in solving the following integration. Thank you in advance.
Integrate[((Sqrt[g*(x + h)/y])^V) * Exp[-u * Sqrt[g*(x + h)/y]/n] * Exp[-L*x], {x, 0, Infinity}]
18
votes
3answers
1k views
How can I use Python's SciPy and NumPy functions in Mathematica to find the minimum of a function?
I have written my code in Mathematica, final aim of this code is to find the minimum of a function.
I found that FindMinimum and ...
0
votes
0answers
16 views
Using FindArgMax in NSolve with dependant variables
I have a function for a current through a series circuit containing a capacitor(c) and a resistor(r) and a battery(Ebatt) when the capacity increases from c0 to c.
...
0
votes
1answer
63 views
Portfolio optimization
Mathematica provides codes for a portfolio optimization https://www.wolframcloud.com/objects/summerschool/pages/2017/AndresLopezMartinez_TE that do not work anymore.
Any reason why?
I have been trying ...
0
votes
0answers
63 views
Simplify a heavy calculation
I'm aware that this may be regarded as too non-specific and with too little information, but I hope that someone will be able to help me nonetheless or to request information which would be imperative ...
2
votes
2answers
65 views
Can't find parameter with findFit NMinimize
I have a data list and a function being to be fitted to the data to get parameters of the function as below. I can't find the parameters a, b, c, d with different below methods. Can you help me to ...
0
votes
1answer
41 views
ArgMax : Variable Domain Error [closed]
I'm attempting to utilize the ArgMax function, but am receiving the error "ArgMax::vdom: Variable domain ... should be either Reals or Integers."
...
1
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1answer
58 views
LinearOptimization duality
I'm solving a linear program using LinearOptimization. I'm curious why "DualityGap" does not return zero (as described in the docs). Here's the code:
...
1
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1answer
76 views
Plot “Findroot” with very complex variables
I ran into an extremely complex "zero problem" and don't know how to solve and plot it. Can anyone help with this, please? [Pi]s and [Pi]r are objective functions, pd, po, qd, qo, and [Phi] (...
0
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1answer
57 views
0
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0answers
71 views
NMinimize for searching global minimum
I have been trying to find global minimum for this equation for some time now.
The equation is quite easy to understand. It is made with sumation of stress equations of points on the border where $σ_{...
2
votes
1answer
49 views
How to use parts of expression as variables in Minimize (NMinimize )?
I want to solve some optimization problem involving matrices.
A toy example related to the problem looks as follows
...
0
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2answers
107 views
How to get mathematica to give an exact answer rather than a numerical approx
I tried // Rationalize but it just gave the same answer
Please help
2
votes
1answer
60 views
Finding the maximum value from the roots of a solution when there is an ambiguity
I have a variable
x = l*Cos[t]*Cos[a] - Sin[t]*Sin[a]
and I want to find the maximum value of x with respect to a, as well as access the roots. I have tried
...
1
vote
1answer
43 views
Nominal variables in LinearModelFit must be specified before continuous variables
I am applying the LinearModelFit to a 90 x 5 matrix, in which the 4th variable is a nominal variable (i.e., x4 is a categorical ...
2
votes
0answers
53 views
How to find the regions for which the derivative of my function changes sign?
I have an energy function of the angles of the electrons' spins. th1 is vector with (2l+2) elements and each element represents the angle of an individual electron spin. I need to eventually find the ...
1
vote
0answers
69 views
What is the best optimization method for the following function?
I have calculated the energy of the electrons as a function of their angles. and I want to find the angles for which my function (energy) is minimized. I have used NMinimize, but the angles I get from ...
1
vote
0answers
43 views
Overriding AccuracyGoal in NMinimize
How can I override the AccuracyGoal parameter in NMinimize? Instead of the evaluation stopping at the required Accuracy, I want it to stop after a specific number of iterations, even if the ...
0
votes
1answer
25 views
NMinimize is not returning values [closed]
I am new to Mathematica. What is the mistake I am making in the following code snippet?
...
0
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1answer
84 views
How to plot a hexagon inscribed on a cylinder in 3D? The cylinder is hollowed out in the form of a hexagon (Mathematica)
I want to plot a hexagon inscribed on a cylinder in 3D using Mathematica.
Edit1: I would like to define its direction by means of a vector
1
vote
1answer
112 views
Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function
I continue to study the topic I started here: Problem with optimal control and Pontryagin's maximum principle
A simple ODE system $(1)$ is given:
$F=\begin{cases} \dot{x}=g \\ \dot{g}=-g+\frac{df}{...
1
vote
1answer
60 views
List of constraints in Minimize
I'm seeking a technique to automate a list of constraints in Mathematica. A sample piece of code is given below; it's designed to take a 3D cube [0, 1]^3, sample 5 points uniformly randomly from this ...
6
votes
1answer
325 views
Problem with optimal control and Pontryagin's maximum principle
For dynamic system:
$\dot{x}=\frac{df}{dx}+u$
where $f=e^{-x^2}$
It is necessary to develop optimal control, minimizing criterion:
$J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $
Algorithm:
We ...
0
votes
1answer
81 views
Problem with RandomSearch option
Solving an optimization problem with Method->"RandomSearch" option
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0
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0answers
55 views
How to perform brute force method with Knapsack /0-1 money-changing problem, with the following table of potential knapsack items
This is the listing item with 400 as Knapsack size...
...
