All Questions
Tagged with equation-solving mathematical-optimization
211
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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:...
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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 ...
- 2,654
2
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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 ...
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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
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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:
...
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8
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2
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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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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&...
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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
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vote
1
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86
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Minimization of an implicitly specified function
exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility
I ...
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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
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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
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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
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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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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 ...
- 4,903
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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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
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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:
$$K c_1 x_1=(1-x_2)(1-x_3)+a_1(1-x_2)x_3+a_2(1-x_3)x_2+a_3x_3x_2$$
$$K c_2 ...
3
votes
2
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209
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Fitting an exponential system
Consider the following system over a periodic array, where $1\leq j\leq n$,
$$
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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1
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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
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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
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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 ...
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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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