Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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My model has not finished evaluating in more than a day so can't test if it works, what is wrong with it?
Hello I have this modified monocentric city model that I have been working on for a while.
Sorry for the long post, I wanted to add the whole code, because it's all connected.
My suspicion is that it ...
2
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1
answer
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Local extrema points of a function of two variables
i need to find local extrema points of a function of two variables, but it doesnt work
FindMaximum[x^3 - 2 y^3 - 3 x + 6 y, {x, y}]
I have this error:
...
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0
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1
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Finding local minimum of a 2D potential
I tried to find a local minimum point of a 2D potential U[\[Chi],\[CurlyPhi]] with both FindMinimum and ...
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Norm adding up residual
For FindFit I want to have a norm that just sums up all residuals.
For the sum of absolute values there is NormFunction -> (Norm[#, 1] &), but I don't know ...
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3
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How can I quickly find the coordinates of key points? [closed]
There are 1000 points in the space. The coordinates are (0,0,0) - (9,9,9). Any point can cover all points on the three straight lines (parallel to the X, Y and Z axes respectively) where this point is ...
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Minimax / Minmax optimization
For the complex polynomial $$P_n(z) := 1+z+\frac{z^2}{2} + \sum_{j=3}^n \gamma_j z^j,\quad z \in \mathbb C.$$ I want to solve the following minimax/minmax optimization problem:
$$\min_{\gamma_j} \max_{...
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Issues with ConvexOptimization and SetPrecision
I am completely new to Mathematica (second day), so do not expect things to look polished.
I am trying to perform a ConvexOptimization over a List/Array (dimensionality ...
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Is there a faster way to solve this linear programming problem?
I need to get a rational solution of the linear constraints
...
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2
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1
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Parametric minimization of a quadratic expression in two variables
I am not an expert in using Mathematica, and I do not understand the following result (apologies if it appears trivial). I want to find the general solution to minimize the following expression over $...
0
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1
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Finding element selected in NMaximize[{Min[...], constraints},{vars}]
How can I determine which element of Min[] is being selected in a NMaximize[{Min[...], constraints},{vars}] problem? For example,...
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When can you guarantee Minimize outputs the global minimum? [closed]
In the Minimize documentation, it's stated that "Minimize will return exact results if given exact input. With approximate input, it automatically calls NMinimize."
What is an approximate ...
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Convex optimization of a least squares regularized objective function [closed]
Given, a vector of observations $\mathbf{y}=(y_1, y_2,\ldots,y_n)$ I am trying to find the soltuion to the following optimization problem:
$$
\min{ (1/2) \|\mathbf{y-x}\|_2^2 + \lambda \|\mathbf{Dx}\|...
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Find the maximum value of the minimum eigenvalue of the matrix
There is a $4×4$ matrix $Q$ where $c,d,e,m,n$ are variables.
How to get the maximum value of the minimum eigenvalue of $Q$?
$Q=$ $$\\\left(
\begin{array}{cccc}
\frac{12058305}{23104}-304 c & -849 ...
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Simplification of long trigonometric expression taking a long time
I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
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Selecting a set of points from a region to maximize the smallest pairwise distance
Suppose, we have a region (say, for simplicity, a unit cube) and a distance function that, given the coordinates of any two points in the region, calculates the distance between them. It is not simply ...
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How to numerically solve an equation
I would like to solve for $r_2$ the following two (independent) equations:
$x_{Min}(a,b,c,r_1,F)=x_{Max}(a,b,c,r_2,F)$ (1)
and
$x_{Min}(a,b,c,r_2,F)=x_{Max}(a,b,c,r_1,F)$ (2)
where $a$, $b$, $c$, $r_1$...
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Plot issue : put a legend instead of a top label
I have an issue about putting a legend consisted of a text and numerical value instead of a label.
For example, with this command line :
...
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1
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Plot issue : bad label ordering with concatenation of strings
I have an issue about a label which is consisted of a variable name [Omega]BD and a numerical value associated.
Firstly, I put the BD subscript to ...
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0
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Find Max Instance Over Permutations
I would like to find the maximum of some objective function over all possible permutations
...
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How to Plot 3D plot for optimized values in Mathematica
I have the following ODE from the paper https://sci-hub.hkvisa.net/10.1016/j.aml.2018.02.016
$y^{\prime\prime}(t)=-ay^{\prime m}(t)+y(t)(b y^{2}(t)-\frac{3}{2}y(t)+\frac{1}{2})$.
The boundary ...
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PlotMarkers in Mathematica with using an iteration scheme
I have the following operator $T:[0,1]\rightarrow[0,1]$ by $Tx=\frac{x}{2}$. I use the following method for two different initial point $x_{0}\in[0,1]$ as $x_{n+1}=Tx_{n}$ $n=0,1,2,3,...$
I have set ...
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How to optimize the $L^{2}$ norm in Mathematica for an iteration scheme and How to plot its 3D graph?
Consider the BVP $y^{\prime\prime}(t)=\frac{3}{2}y(t)^{2}$ with boundary conditions $y(0)=4$ and $y(1)=1$. The initial iterate is in this case $x_{0}=4-3t$. The higher iterates are given by the ...
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Minimizing and marginalizing in Mathematica
Suppose there is a chi-squared function of several parameters, f(x,y,z),
and I have to fit one parameter, say "x", while the rest "y" and "z" have to be dealt with in a ...
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Please I need help to define a function of two variables (t,x)!
Let's define the following function:
f[t_, x_] = t^2 + t*x*(1 - x)
such that $x \in (0,1)$ and `$t \in (0,0.02)$
The problem is when I want to define the following ...
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Solve two equation by fixed point iteration method
I am tryin to reproduce the figure.2 of this paper. In order to obtain this plot, I need to find the global minimum of equation.(7) or equivalently solving two coupled equations of $\frac{\partial \...
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How do I find the minimum and maximum values of a function of two variable with constraints? [closed]
The question is find the minima and maxima of the function
$$f(x,y)= x^2+5y^2+11x-12y+30$$
on $(x^2)/81+(y^2)/49 \leq 1.$
I've been trying to use FindMaxValue and <...
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Why do I get NMinimize::nrnum error?
I have this minimization program and although I've restricted my variables to be non negative, I get a nrnum error in the NMinimize step. I'm guessing this is what ...
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Maximizing arbitrarily scaled step function
I am attempting to maximize a function dependent on a single variable (x) that contains multiple parameters. The case of a simply loaded beam with discontinuities in the loading. However so far I have ...
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Finding maximum of 2D interpolating function as a function of one of the variables
I am solving a 2D PDE in space and time b(r,t) and would like to find the maximum value of b in space as a function of time t.
Using the solution for maximising a 1D interpolating function from here, ...
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Optimal command pipelining that maximizes total value in a given time duration
Consider I have two types of commands A and B which can be pipelined. Each of these types have a certain time duration and a value associated with it.
For example,
...
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Differences between minimization functions?
There's more than 20 functions having to do with minimization
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Code Producing FindMinimum::nrnum; how do we fix it?
Suppose $A=\left\{\sqrt{m}:m\in\mathbb{N}\right\}$ and $S\subseteq A$:
I wish to create a code which finds:
$$\min\left\{c:\forall(d\in S)\exists(c\in A)\left(c/d\in A\right),\max(S)\le c \le \prod\...
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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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problem In NMinimize and large number of variables and constraints
I Try to solve TSP problem by writing the linear program of this problem (I know that FindShortestTour Function can solve it but I need to solve it manually), I generate the linear program correctly ...
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Expressions using matrix variables in SemidefiniteOptimization
The SemidefiniteOptimization function allows one to specify the region for the optimization variable, such as in
...
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extremum points
I'm trying to find Min and Max points of the polynomial below, but it seems that the expression is very complicated to mathematical, I've tried a numerical function, such as NMinimize, NRoots, Solve, ...
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How do I use a FunctionCompile(d) function in FindMInimum
Suppose I would like to speed up the function in FindMinimum[function[variables],startingPoint] by compiling function
I've constructed a minimal working example to describe what I would like to do.
...
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How do I find the maxima of the function x+y such that x^2+y^2=1? [closed]
It is a simple question. I am trying to maximise x+y for coordinates {x,y} that lies on a circle of radius one. I tried using FindMaximum.
...
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Table of time-varing calculation slower to the point of kernel blowing up
There is a complicated function obtained by numerically solving a pde, let us call it $u(t,x,z)$.
For this $u$, I want to calculate the global maximum of $u^2$ at a fixed position of $z$, and plot ...
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Need to find a unique mathematical expression (not in documentation) that is as short as possible but takes a good amount of time to evaluate
I am writing a public ResourceFunction and I need a good clever use case that should not appear to emulate any examples in the official documentation but will ...
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Easier way to find integers for complex^complex
If I have (a+b I)^(c+d I) and the result is e+f I
a,b,c,d should be integers
e >= 2 or e <= -2
f so close to zero as possible .. this is the object function I want to minimize
How to do this in ...
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Fitting data in a matrix
Consider the 'm' matrix: Link to 'matrix.dat': https://drive.google.com/drive/folders/1COdMCCBKq85vMDj6Jrb2qqoUlE9eTk6w?usp=sharing
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Solve an equation
I have this equation in terms of x0 and I need to find x0 in terms of Theta .
...
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Accumulate matrix elements
Consider the 'm' matrix:
Link to 'matrix.dat': https://drive.google.com/drive/folders/1COdMCCBKq85vMDj6Jrb2qqoUlE9eTk6w?usp=sharing
...
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Solving numerically Pdes and Odes and Iteration processes
Dears, I have the following equations: $x^{\prime\prime}(t)=\frac{3}{2}x(t)^{2}$ with $x(0)=4$ and $x(1)=1$. The exact solution is $x(t)=\frac{4}{(1+t)^{2}}$. Now the corresponding operator is
$
Px=x+\...
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It seems that ConvexOptimization does not attain the optimal value
I am trying to implement the concrete example of formula (11.20) Boyd & Vandenberghe, page 580.
Therefore, we have computed a point that satisfies many
(m − r) of the inequalities, i.e., we have ...
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Correct code for 4th differential equation
How to code and solve the following equation in mathematica.
d^2/dx^2(x^2d^2u/dx^2)+b^2u=0
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How is Mathematica minimizing correlation exactly with linear constraints?
I made a random data matrix as
data = Table[Random[], {i, 5}, {j, 5}];
In my case it was
$$ \left(
\begin{array}{ccccc}
0.951203 & 0.546669 & 0.86928 &...
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How to get x and y values and function of xy pairs (H[x,y]) from Histogramlist?
So I have generated a set of random data points as shown below
sample1 = RandomVariate[BinormalDistribution[{0, 0.4}, {1.2, 1.2}, 0], 250];
From the sample, I ...
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