Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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Relationship between two minimization problems
In a previous post of mine (here), I raised the question of how to identify points on a specified frontier. My approach to it was the following:
Let $\mathbf{A}$ be a ${n\times J}$ matrix with $A_{ij}...
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1answer
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Find maximum of x given a bunch of constraints
Trying to find maximum of x given that '''0<=x<=3''' and some other stuff. This works fine:
Clear[x, y]
FindMaximum[{x, 0<=x<=3}, x]
But this does ...
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1answer
28 views
Function of Maximum and Minimum Functions of Two Functions
I try to answer this question The Maximum and Minimum Functions of Two Functions
I wrote the following code
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Numerical maximization
I am facing a numerical maximization problem with constraints.
Using Method -> {"RandomSearch", "SearchPoints" -> 3}, AccuracyGoal -> 2 often does not find ...
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31 views
Is there a feasible computation?
I have to find the values of $p_1$ and $p_2$ which minimizes the expression $G$. However, when I took the partial differentiation of $G$ with respect to $p_1$ and $p_2$, the equations I obtained were ...
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1answer
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Nested optimization problem 3
thanks to Ulrich Neumann I am getting close to the solution of my problem...
However, Mathematica tells me that no points satisfy the constraints of the following problem:
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1answer
30 views
Nested optimization problem 2
I would like to solve a maximization problem which itself depends on a maximization. I came up with this code,
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1answer
39 views
Nested optimization problem
I would like to solve a maximization problem which itself depends on a maximization.
I came up with this code,
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1answer
59 views
Linear map of unit cube (generalized)
This question is a slight generalization of this question.
Let M be a fixed rational m $\times$ ...
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1answer
91 views
Minimize fails to find a minimum [on hold]
I am trying to find, analytically, the $\theta,\phi$ that minimize the function U($\theta,\phi$)
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Get default values used in an Option of a NMinimize Method
I fear the answer is trivial, but I have extensively searched without any success.
Say I perform a Nminimize minimisation using the Method "Simulated Annealing", e.g. the following from the ...
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1answer
78 views
The Maximum and Minimum Functions of Two Functions
Suppose I have two functions f(x,y)=1 + 2*x +3*y^3 and g(x,y)=y + x^2. I want to have maximum function of ...
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Constrain values to numeric during Minimize
I understand, that similar questions have been asked before, but I am absolutely new to Mathematica and can not solve it myself:
In nuce it is the following: I want to calculate
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3answers
102 views
Constraint of NDSolve with an integral of the solution
I'd like to use NDSolve and to make a constraint with an integral.
For example, take the very simple : $$f'(x)=-f(x)/x_0 $$
the solution is $$f(x)=f_0 e^{-x/x_0} $$
And $f_0$ is given by : $$\int_0^...
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1answer
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error for NMinimize with Parameters in the form f[a_]:=NMinimize
I'm trying to write a function of a variable as the argument of a minimization where that variable comes to play.
Here is the code :
...
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1answer
29 views
Parallelizing FindMinimum
I have complicated 6-dimensional function to optimise. Using FindMinimum works all right, but takes a few minutes. Considering that I want to check multiple starting points, I'm looking at run times ...
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How to fit a spline (not interpolate) through points in 3D?
I have coordinates of points in 3D and want to fit a spline through these points. I found a least square approach for 2D case:
https://demonstrations.wolfram.com/...
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1answer
68 views
How to include measurement error in FindDistributionParameters (using maximum likelihood)?
I am trying to fit a non-standard PDF to data using FindDistributionParameters. My custom distribution is defined like this:
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2answers
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Optimize with constraints
I want to find the smallest $k$ such that $kx^2 \ge (\sin(x)-x)^2$ for all scalar $x\in[a,\ b]$? Obviously, I can do it analytically, but how can I do it (symbolically) in Mathematica? I am new to ...
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2answers
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Find optimal BezierFunction
For a given set of points (examplary quadrant)
n = 5; (* number of inner points*)
p = Table[{Cos[φ], Sin[φ]}, {φ, Join[{0}, RandomReal[{0, Pi/2}, n], {Pi/2}]}];
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The problem in finding a connected path through square lattice
I have a LxL square lattice. I randomly chose some points on this lattice and take them as my points. I want to find a connected path from left(0) to right(L). Below is my code:
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NMinimize with real solutions, problem in the resolution and criteria for other ways to solve equations
I have multiple parts in my question. You are welcome to answer to any of them :)
Part 1 :
I have 3 equations $p(x_1,y_1)=p(x_2,y_2),\mu_x(x_1,y_1)=\mu_x(x_2,y_2),\mu_y(x_1,y_1)=\mu_y(x_2,y_2)$. I'm ...
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NMinimize and large number of unknowns: avoid explicitly writing the list down
I have set up a rather large minimisation problem and it works well, if not for one nuisance.
I need to often change the number of variables to be given to NMinimize: clearly it is rather impractical ...
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Different results for different LP Methods
I am trying to utilize the Farkas dual as a certificate of primal infeasibility. The goal is to solve the problem
$$\min_{\textbf{y}} \textbf x\cdot \textbf b \text{ subject to } \\ \textbf 1 \geq ...
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1answer
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How to use StepMonitor in NMinimize when using vector variable
Bug persists through 12.0
For example, when I call this code
...
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1answer
95 views
Implement gradient method in functional programming style
I implemented the gm for quadratic function in Mathematica, but it looks like more in an OOP style, as the pic shows.
How to rewrite it in Mathematica style? I tried with following code:
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Making a density plot for an expression
I have defined a function the energy $E$ of a given system by
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49 views
LinearProgramming with constraint on result
I need to solve a bunch of Diophantine Equations that takes so looong with FindInstance/Reduce, so I tried LinearProgramming and it's very fast. Here is a simple one:
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2answers
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Check whether a given quantity is negative
Given four numbers $n0, n1, n2, n4$ such that $n1+n2+n3+n4 = 1$. How can we check the sign of $A - 2 B$ (where $A$ and $B$ are defined below), i.e., whether this quantity is positive or negative?
<...
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Apply Conditions on the Derivative of a Model with More Equations than Data in FindFit
Looking to combine the two approaches from these two posts here:
How to Add a Constraint on the Derivative of the Model in FindFit
How to fit 3 data sets to a model of 4 differential equations?
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1answer
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How to have NonlinearModelFit not evaluate a function too early?
This is a follow up of my previous question How can I define the following function for arbitray values of the arguments? that received no attention so here I will try to be more concise with the ...
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Status of DualLinearProgramming
DualLinearProgramming is referenced in this tutorial
tutorial/ConstrainedOptimizationLinearProgramming
It exists in ...
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1answer
43 views
How to Add a Constraint on the Derivative of the Model in FindFit
I would like to add constraints on a model and its derivatives and then use FindFit to fit some parameters. An example is below:
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1answer
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FindFit or NMinimize? Fitting a System of ODEs to Long Time Behaviour
I am looking to fit a model composed of a system of ODEs to a long term behaviour given by a single data point of the final steady state of the system (e.g., x[1000] == pi/2). I have tried using both ...
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65 views
FindMinimum giving wrong answer [closed]
I have a very simple problem that Mathematica is giving a wrong answer to. I want to minimize the following function:
$\frac{3+t^2+6\theta +3 \theta^2}{6 t^3}$ in $\theta$ and $t$.
Now, plotting the ...
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1answer
265 views
Finding local minima of an energy defined by integration
This question is also asked here and here.
I would like to reproduce the two solid curves in Fig. 1a of this paper. The total energy is given in Appendix A, and the curve is obtained by minimizing ...
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1answer
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Solve the vector-matrix equation. Minimize the length of the desired n-dimensional vector
There is the following vector-matrix equation.
where C - nonzero constant.
[x1 x2 ... xn] - vector of real numbers.
M - matrix of real numbers of dimension n x n
It is required to find a vector $x$...
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Univariate Gaussian Splitting
I would like to experiment a bit with univariate Gaussian Split libraries.
This is essentially a constrained non-linear optimization (minimization) problem.
There are multiple formulations of this ...
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1answer
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Using NMinimize with Table to plot an energy
I would like to reproduce the solid blue line of Figure 2a in this article. For this, I have used the code found here. Notice, however, that I am not succeeding. Could you help me? Here is my code:
<...
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1answer
108 views
$\min \int_{0}^{\infty} (a f'(x)^2+b f(x)^2+c |f(x)|) dx$
Can Mathematica solve
$\min_{f(x) s.t. f(0)=f_0} \int_{0}^{\infty} (a f'(x)^2+b f(x)^2+c |f(x)|$)dx ?
I tried
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1answer
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Plot with substitution of domain values before evaluation of function
I have a function of two variables $f(x,y)$. I find the maximum value of $f(x_0,y)$ by first substituting the value of $x=x_0$ and then maximizing in the range $0<y<1$.
My question is: How to <...
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5answers
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If someone would want to think about the question: mathematical-optimization “Banknote”
I solved the puzzle of IBM Ponder This September 2019 by my code written with mathematica.
I would like to share this code after the solution that will come as soon, and discuss it.
In the meantime, ...
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2answers
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0answers
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Time optimization of motion using mathematica
Let us say I have a double pendulum, with the torque equations and the initial and final poisition of the end point of the pendulum. I have constraints on the maximum and minimum values of torques. I ...
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4answers
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FindMinimum where variables are Integers
I wish to find the minimum of a function where the variables are integers. Here is a simple minimum working example (my actual function is much more complicated).
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1answer
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How can I find the minimum and maximum output of a function and specify the valid ranges and steping of each variable? [closed]
I am a software developer, and it has been far too long since the last time I've needed to do any math this complicated. I've forgotten a lot of the proper terminology, which has made finding answers ...
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1answer
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How to get ReplaceAll to happen before function call
I have a problem I am attempting to solve with NMinimize.
I have a scoring function, which will give me a final score. The problem has many variables, so instead of having them as parameters, they ...
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2answers
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Using MinValue with NDSolve
A simplified example looks like this. The basic idea is to maximize fHelper by adjusting \[Alpha] for each ...
