All Questions
Tagged with equation-solving mathematical-optimization
52
questions with no upvoted or accepted answers
4
votes
0
answers
137
views
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 ...
- 777
2
votes
0
answers
218
views
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 ...
2
votes
0
answers
192
views
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
2
votes
0
answers
59
views
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 ...
2
votes
0
answers
80
views
For any countable totally-ordered $A$, how can mathematica show my choice function gives a unique collection of finite sets whose union is $A$?
Suppose $A=\sqrt{\mathbb{Q}}_{>0}$. We want a unique $\bigcup\limits_{i\le j}A_i$ for $i,j\in\mathbb{N}$ such that $A_i$ is finite, $A_i\subseteq A_{i+1}$, and $\lim\limits_{j\to\infty}\bigcup\...
- 81
2
votes
0
answers
80
views
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 ...
- 1,285
2
votes
0
answers
47
views
Solving an equation with a maximum variable
I've the following equation that I need to solve:
...
- 287
2
votes
0
answers
80
views
Using FindMinimum to solve equations as constraints
As suggested here, a system of equations can be seen as constraints in a minimization procedure with a zero cost function.
For instance:
...
- 14.4k
2
votes
0
answers
707
views
Numerically/Analytically Solving a System of Equations
I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
- 283
1
vote
0
answers
225
views
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
vote
0
answers
61
views
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:
...
1
vote
0
answers
97
views
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 ...
1
vote
0
answers
105
views
NSolve cannot solve. 3 equations in 3 variables
I'm trying to numerically find the critical points of the following function in 3 variables
...
- 471
1
vote
0
answers
45
views
Finding analytic expression with replacement rules
I have a function defined as
f[k_]:= Maximize[{(x^2/(1+x^2))((1-x^(2k))/(1+x^(2k+1)))^2, 0 <= x <= 1}, x]
I would like to find an analytic form of $f$ as a ...
- 11
1
vote
0
answers
38
views
How to analyse huge output from Reduce systematically?
I have a constrained optimization problem, looking for Nash equilibria. I use the KKT conditions programmed using Reduce to solve it. For the general case I get a very large output, with more than 100 ...
