Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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Error when calling NMinimize on an InterpolatingFunction which depends on parameters
I'm trying to solve a basic calculus of variations problem numerically, by minimizing an integral over an Interpolating Function.
Basically this:
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Supply gradient to FindMinimum subject to constraints
FindMinimum supports explicitly supplying the gradient (as well as the Hessian) via the Gradient (resp. Hessian) option. However,...
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Singularity or stiff system in ParametricNDSolve
I have following parameters and equations(it's a complex one, please check it :) ):
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63 views
Using SemidefiniteOptimization with a partial-ordering constraint
I'm running into an issue enforcing a particular constraint on the variables of a SemidefiniteOptimization problem (I'm using Mathematica 12.3).
Specifically, it seems that if a matrix $A$ and a ...
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Nested NMaximize
I am trying to simulate a Stackelberg Competition model in Mathematica, where the problem is:
Player 1 has utility function f[x, y, z] and plays first. He can ...
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Optimization when actively working with the NDSolve command
Lagrangian of three-mass system with Mathematica
Based on the Lagrangian of a mechanical system, we can obtain a system of equations of motion. These equations can be explored numerically using the ...
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Why increasing PrecisionGoal and WorkingPrecision is deteriorating my results
I am minimizing a variable subject to many very complicated constraints, like
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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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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 ...
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111 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 ...
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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:
$$
m:= ...
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Maximization of piecewise function
I'm trying to maximize piecewise functions with parameters but haven't been able to do so. Here is a minimum example:
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General::munfl - Precision lost in LinearModelFit
I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3)
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NMinimize over a list of integers
I'd like to minimize some function (of 3-4 variables) over a big list of integers, but not consecutive. Like arr = {5, 10, 7, 101,...}
I did not understand this ...
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37 views
Trouble using NMinimize [closed]
I am trying to minimize five function at the same time. I am running in some trouble minimizing this function, as since I am not that familiar with Mathematica I really do not know what I am doing ...
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Low Tolerance making wrong behavior of LinearProgramming?
I was working on a code that needs to check feasibility of LP problems. I visited Checking linear program feasibility? and used the code. With this code, since there is 1 at the last position at every ...
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103 views
How to solve a nonlinear system of equations with exponential terms
I want to solve this parametric nonlinear system of equations in Mathematica:
$$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:
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1answer
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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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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 ...
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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 ...
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1answer
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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:
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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 ...
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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 ...
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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 ...
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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 (...
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Calculating my code for higher values of `k`?
How do I calculate the mean of A for higher values of k
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361 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}...
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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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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}...
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1answer
128 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=...
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4answers
151 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 ...
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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}]
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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 ...
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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.
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1answer
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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 ...
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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 ...
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2answers
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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 ...
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1answer
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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."
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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:
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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] (...
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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_{...
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1answer
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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
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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
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1answer
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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
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
