All Questions
Tagged with equation-solving mathematical-optimization
33
questions
19
votes
2
answers
1k
views
Determining the default Method used in optimization and root-finding algorithms
Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, <...
- 113k
-1
votes
3
answers
7k
views
How do I determine the maximum value for a polynomial, given a range of x values?
I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
- 99
8
votes
2
answers
388
views
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
4
votes
1
answer
6k
views
Finding the Minimum value of an interpolating function
I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function.
For instance the below code generates an interpolating ...
- 5,351
18
votes
4
answers
1k
views
Find the equidistance curve between two curves
I have three function $f(x)=x^x$, $g(x)=\ln(x)^{\ln(x)}$, $h(x)=\ln(x)^2$ and I want to find (numerically) $C$ the center of the circle tangent to the three curves.
I think that one way is to find ...
- 499
14
votes
1
answer
967
views
Solving optimal control problem when input is constrained
Given a linear time-invariant system:
$$x'(t)=Ax(t)+Bu(t)$$
with initial state $x(0)=x0$ and final state $x(T)=xT$.
The performance measure to be minimized is:
$$∫_0^Tu(t)^2dt$$
The most important ...
- 141
10
votes
2
answers
1k
views
Problem with optimal control and Pontryagin's maximum principle
For dynamic system:
$\dot{x}=\frac{df}{dx}+u$
where $f=e^{-x^2}$
It is necessary to develop optimal control, minimizing criterion:
$J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $
Algorithm:
We ...
- 2,444
6
votes
2
answers
339
views
Counterpart of Maple's LSSolve in Mathematica
I am a great fan of Mathematica. Unfortunately, due to some specific tasks I had to move to Maple. I think it's my lack of info that is not letting me do those tasks. That is why I am asking some ...
- 339
3
votes
1
answer
2k
views
wrong use of _?NumberQ?
I am having trouble with a numerical exercise. Here's a simplified version of my problem.
I define two functions to find the solution to two constrained maximization problems:
...
- 335
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 ...
-1
votes
1
answer
106
views
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 ...
7
votes
3
answers
884
views
Not able to get a solution to a Lagrange Multiplier Equation
I assigned several constrained optimization problems to my calc IV students to solve with Mathematica, but this one is being stubborn.
The function to optimize is: f(x,y,z) = y Exp[x-z]
with the ...
- 71
5
votes
2
answers
317
views
Find maximum of the output from reduce
I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be ...
- 295
4
votes
1
answer
351
views
best way for finding approximate root of monotonic sawtooth like function
First I will generate such kind of monotonic sawtooth like function called func
...
- 17.2k
4
votes
3
answers
1k
views
FindRoot constrained to maximum
I am using FindRoot to find the local maximum op some function, by examining where its derivative is zero. However, keeping the starting value the same, sometimes <...
- 1,605