All Questions
Tagged with equation-solving mathematical-optimization
211
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32
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Find the function for a decision variable
I'm currently trying to find the equation for a decision variable from a total profit equation using Mathematica. From what I've read, I can use the solve function to do this. Here's a example i found:...
- 1
4
votes
1
answer
136
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Findroot :unable to find a solution that meets the convergence criteria
The stationary solutions of the Klein-Gordon equation refer to time-independent solutions, meaning they remain constant over time. For the non-linear Klein-Gordon equation, you are discussing:$$\frac{...
5
votes
1
answer
233
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Colouring Bifurcation Diagram
I need to plot the bifurcation diagram for the function given below.
g[x_, r_] := 6 x^2 + r x^4 + x^6
Plot[g[x, -4.9], {x, -2, 2}]
Bifurcation
Code for ...
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2
votes
0
answers
218
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Solving `Integrate` of `InterpolatingFunction` from an `NDSolve`
I am interested in solving a system of Differential Equations, particularly
u''[\[Tau]]=-f[t]u[\[Tau]]
This system has for initial conditions $u(0)=1/\sqrt{2\cdot ...
0
votes
0
answers
101
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Solving an optimization problem with rather complicated functions
I'm trying to solve the following optimization problem.
\begin{aligned}
\max_{e, s} \quad & v=\frac{(\lambda + i)U_{emp}+(1-e)U_{unemp}}{i(1-e+\lambda+i)}\\
\textrm{s.t.} \quad & \lambda = \...
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3
votes
1
answer
201
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How to find a unimodular integer matrix $T$ satisfying $T^\top A T=B$ given symmetric integer matrices $A,B$?
Given two unimodular symmetric integer matrices $A$ and $B$,
I asked how to find a unimodular integer $T$ that satisfies this nonlinear relation between $T$ and $A,B$ like this in Mathematica:
...
- 251
8
votes
2
answers
388
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Given square matrices A and B, how to solve T obeys Transpose[T]. A . T = B?
Dear Mathematica experts,
Given two square matrices, A and B, how do we use Mathematica to solve a matrix T such that T satisfies this matrix equation? (Here we have A,B,T $\in$ general linear matrix ...
- 251
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0
answers
37
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Use Fitting Parameter from Solve or Nminimize with LinearModelFit
Im Trying to minimize a function by varying parameter "a" with Solve or Nminimize. The Problem is that "a" is dependent on my parameter "R" which is dependent on "a&...
0
votes
0
answers
59
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How to speed up maximization of the Solve output?
I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains.
Here is the code
...
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1
vote
1
answer
69
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Find an instance satisfying equation
I have the following equation with two variables xi and nu.
...
- 496
1
vote
1
answer
86
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Minimization of an implicitly specified function
exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility
I ...
- 1,883
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0
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92
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Why doesn't NMinimize work with NSolve?
Why does NMinimize throw the error and how to fix it?
...
- 1,883
2
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3
answers
288
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How to solve this equation over the integers with Mathematica?
I try to solve with Mathematica 13.3.1 on Windows 10 the problem $$x^2+2^{x^2+1990}-y^2=2^{y^2+y}+y-1990\land x+y>1990,\, x\in \mathbb{Z},\,y\in \mathbb{Z}$$
which originates from Bauman Moscow ...
- 27.3k
0
votes
2
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109
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Why can't NSolve find values that FindInstance can?
I am trying to solve for \[Epsilon], given three input paramters n, x and ...
- 496
1
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0
answers
225
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Help with code for impulsive optimal control problem
I am using Mathematica 13.3 to numerically solve/generate numerical plots for my impulsive control problem.
The optimal control problem is:
T is time from0 to T where T is the terminal time
K(t), B(t) ...
- 11
1
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0
answers
61
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Finding the symbolic root of a non-linear function with fractional exponents
Define $f(x, a, t) = (x-t)^a - \frac{x^2}{2}$ where $x>0$ is the main variable of interest and $\alpha \in (0,1)$ is the parameter of curvature:
...
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49
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Optimization problem with complex and real values
I have the following optimization problem:
$\underset{{{a}_{1}},...,{{a}_{m}}}{\mathop{\max }}\,\parallel \sum\limits_{n=1}^{N}{{{a}_{n}}}{{\varpi }_{n}}{{e}^{j{{\theta }_{n}}}}{{\varphi }_{n}}{{\...
2
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192
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How to approximate an exponential series?
Consider the following expression
$$
y_j= \sum_{k=0}^{L} \frac{e^{-\sum_{i=-k}^k(k-|i|)x_{j+i}}-e^{-\sum_{i=-k}^k(k+1-|i|)x_{j+i}}}{\sum_{i=-k}^k x_{j+i}}\tag{1}
$$
for $1\leq j \leq L$. Given smooth ...
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1
vote
1
answer
130
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Minimize is returning unevaluated for a simple positive integer domain problem [closed]
I don't understand why the following Minimize code is returning unevaluated. I believe I have it coded properly and the expected minimum is $x=14$ and $y=1$.
<...
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1
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197
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4
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2
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126
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Representing pairs of values that lead to a constant
I have the following expression:
$Q=\frac{\sqrt{rc}}{1+r(1+K)}$
Q and K are constant values. Basically I want to plot a graph that shows me all the combinations of r and c that verify the equation. ...
1
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0
answers
97
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Optimizing my code to solve nonlinear system
I have solved a non-linear system using Eliminate[] and Solve[], using a really nice answer found here I am able to use ...
0
votes
1
answer
72
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Find solutions after using Eliminate
I have used Eliminate[] to reduce a system of equations as found here, I then proceeded to verify that indeed my system has zeros using this code. My question is, ...
-1
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1
answer
106
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Solving Nonlinear System
I am solving a $3X3$ non-linear system (posted also in mathematics).After some simplifying assumptions it looks like this:
$$K c_1 x_1=(1-x_2)(1-x_3)+a_1(1-x_2)x_3+a_2(1-x_3)x_2+a_3x_3x_2$$
$$K c_2 ...
3
votes
2
answers
209
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Fitting an exponential system
Consider the following system over a periodic array, where $1\leq j\leq n$,
$$
y_j= \sum_{k=0}^m \frac{e^{-\sum_{|i|\leq k}(k-|i|)x_{j+i}}-e^{-\sum_{|i|\leq k}(k+1-|i|)x_{j+i}}}{\sum_{|i|\leq k} x_{j+...
- 4,903
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votes
1
answer
91
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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?
- 4,903
2
votes
1
answer
55
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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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2
votes
1
answer
101
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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 ...
- 315
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1
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281
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Solving an equation involving exponential function
I have an equation
$$ c \tan \left(\theta_{\mathrm{OPT}}\right)+\frac{a b A \exp \left(-b\left[\theta_{\mathrm{OPT}}-a\right]\right)}{\left[a \exp \left(-b\left[\theta_{\mathrm{OPT}}-a\right]\right)+1\...
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2
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86
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how i put condition to sure that values of outputs in FindRoot?
i want to put condition in this like x>0,0<y<1
FindRoot[{Exp[x - 2] == y, y^2 == x,x > 0 && 0 < y < 1}, {{x, 1}, {y, 1}}]
but it dosen't ...
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0
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54
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Finding values of constants for which 1st and 2nd order derivatives of a function vanish
I'm trying to find critical values of some constants $v_c$ and $T_c$, for which holds the equality below:
$$\bigg(\frac{\partial P}{\partial v}\bigg)\biggr\rvert_{v=v_c,\; T=T_c}=0,\quad \bigg(\frac{\...
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1
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2
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181
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How to find the equation of a curve which is not symmetric [closed]
I need to find the equation of f1(x) by these three points (5,4) (2,5 , 0) (0, 1,5). I think it is not a standart symetric parabola.
1
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1
answer
85
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Find binary vector within fixed distance to reference vector that maximizes the number of distances to a set of vector that are below a threshold
Input: A binary reference vector $r$, a multi-set of binary vectors $S$, and a distance function d between binary vectors of equal length. Assume that $r$ and all vectors in $S$ have the same length.
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1
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90
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Real valued solution
I want to obtain the critical points or if you like a real solution for the first derivative of the function set to zero, and the second derivative also vanishes of the function :
...
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2
answers
75
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Find min value of a complex Root function [closed]
Could someone tell me how to obtain the min value of this function when lambda is between 0 and 1:
...
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1
vote
1
answer
132
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Find the maximum of a given function
I calculate a target function f about two variates a and b.
...
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4
votes
1
answer
583
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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 ...
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0
votes
0
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107
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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 ...
- 135
1
vote
1
answer
242
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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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0
votes
0
answers
65
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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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3
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1
answer
201
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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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2
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3
answers
270
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How to prove or disprove an inequality with Mathematica?
I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$ \frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid.
Here are my unsuccessful attempts.
<...
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1
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181
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How to find the value which minimises the residual sum of squares
I have 3 equations with 3 parameters(unknowns). I would to solve it using newton raphson method. I want to use initial values (parameters) for the Newton Raphson
procedure as the value (parameters) ...
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0
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36
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Which result is more reliable in NMaximize in the given code? with `WorkingPrecision` or without it?
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
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votes
2
answers
216
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How to calculate the maximum value of $x $ which satisfy the conditions $g(x,y)=0$ and $f(x,y)>1$?
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
- 749
1
vote
2
answers
323
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Mathematica: How can I solve the problem "The Kernel Local has quit (exited) during the course of an evaluation"
I am using a Mac Book with Monterey and 16GB RAM for a calculation with 2 nested For loops.
I am relatively new to Mathematika and still trying to learn the language properly, so I hope the problem is ...
4
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0
answers
137
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Solving or Minimizing the Norm of the matrix equation $M^TAM - M^TB - B^TM =C$
I am trying to solve the matrix equation $M^TAM - M^TB - B^TM=C$ where I know A, B and C. My unknown matrix is M which has the special form that all the rows and columns sum to zero.
i.e. I have four ...
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1
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74
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Formalization of one optimization problem or solution of inequalities - Part №2
Continuing the question: Formalization of one optimization problem or solution of inequalities
Let's consider a more complex problem. We have two polynomial:
$p_1=A_2t^2+A_1t+A_0$
$p_2=B_2t^2+B_1t+B_0$...
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2
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1
answer
79
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Formalization of one optimization problem or solution of inequalities
I have polynomial:
$p=A_2t^2+A_1t+A_0$
$A_0=(x^2-y^2)+xz$
$A_1=x^2+y^2+z^2+\sin(x)$
$A_2=x^4+y^3+z^2$
$x,y,z$ - parameters, moreover $z$ - the value of which varies in the range $[0,1]$.
Polynomial $p$...
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votes
2
answers
215
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Min and Max of a function
I need to obtain for what $a_i$'s the function:
$$a_1 \ln (\sqrt{2\pi e} s_1) + a_2 \ln (\sqrt{2\pi e} s_2),$$
has a maximum and minimum, under the constraint $a_1 + a_2 = 1$; also, $s_1, s_2 > 0$.
...
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