All Questions
Tagged with equation-solving mathematical-optimization
211
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
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
9
votes
3
answers
272
views
FindRoot evaluates the exact same point multiple times. Why?
This is a follow-up question to this question.
Let's say we want to minimize the following function f wrt. x and ...
- 3,871
8
votes
3
answers
3k
views
How to find the maximum value of an integer that satisfies some inequality
Consider the following Mathematica expression:
Reduce[2^j/(j + 1) <= 10, j, Integers]
which outputs:
...
- 423
8
votes
2
answers
1k
views
Finding the least positive integer satisfying a quantified statement
I'm studying the convergence of the sequence of functions $f_n:[0,1]\subset\mathbb{R}\to\mathbb{R}$ defined by $$f_n(x)=n^2x(1-x^2)^n$$ for $n\in\mathbb{N}$. These functions converge pointwise to the ...
- 205
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
8
votes
1
answer
3k
views
Solve Lagrange multipliers optimization problem
I have two nested solid figure, where $V(a,h,\tau)$ defines the volume and $A(a,h,t)$ defines the surface. The outer solid figure is parametrized in $a_s$,$h_s$ and $t_s$ (they share a common center). ...
- 377
8
votes
1
answer
1k
views
Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations
The formal problem
The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
- 609
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
7
votes
1
answer
190
views
How to generate optimal solution and order the rest
This is a decimal maze, you start with 100 points and you must choose the path that gives you the highest score.
Rule: You should not go twice for the same point and the same segment.
My question: Is ...
- 149
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
5
votes
4
answers
1k
views
How to find maximum/minimum in `ContourPlot`?
The ContourPlot of Sin[x^3 + y] - 2 Cos[x y]==0 has a maximum around (-1.8,-2.3), see figure ...
- 4,679
5
votes
2
answers
438
views
Optimum number of cog teeth for two step helical gearbox
Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I.
I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
- 492