Well, I found the solution by shifting.
Actually, the result has ##2^N## cases equivalent to the number of combinations of ##N## binary variables. Instead of using ##2^N## binary variables for each of the ##2^N## cases, I want to use ##N## binary variables and map them to the results and find...
The worse thing is that I even do not know if a linear mapping for such a problem exists or not.
If one can prove that it exists, then half of the problem is solved. Even if I know that such a map does not exist I will start modeling my problem from scratch in a different way.
Using matrix...
Depends on the index of the elements in ##\mathbf{e}##.
If we start the index from left and from zeor then,
v = [ 1 0 1 ] = 5 → (make the (5+1)-th element of ##\mathbf{e}## equal to 1 where the index starts from zero and from left) → ##\mathbf{e} = [0 \quad 0 \quad 0 \quad 0 \quad 0 \quad 1...
Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...
Well, I am going for simulated annealing but I have some questions regarding the implementation of this algorithm.
I have a couple of constraints for ##M##, like ##\sum_{j \in \mathcal{N}} m_{i,j}=1## and some more.
I think I have to first find a feasible ##M## based on my constraints and then...
Thanks. "simulated annealing" is a good candidate to use. I will work a bit more to see if I can find an easier way, preferably in an standard optimization form.
The problem comes from distributed control for resource allocation in a multiagent system. When an agent uses a resource, the...
Thanks, ##N## is around 20.
"brute force" should work but I am looking for a more efficient way to solve the problem.
Actually I am trying to find a way to formulate it as an standard optimization problem.
Hello, I am working on an optimization problem but I am not sure if the problem can be formulated and solved with conventional solvers.
Assume the minimization problem for a set of elements ##\mathcal{N} =\{ 1,\dots, h, \dots, i,\dots, N \}##
$$
\mathrm{minimize}\quad C = \sum_{i=1}^{N}...
Dear Friends
I have a question about linear programming. It would be great to have your comments or suggestions.
Consider the followings
\begin{equation}
\\
Y = [y_{1}, y_{2}, \cdots, y_{n}]
\\
G = [g_{1}, g_{2}, \cdots, g_{n}]
\\
\textbf{X} =
\begin{pmatrix}
0 & x_{1,2} & \cdots & x_{1,n}...
Dear Dickfore, another question. In the last condition:
the function f depends on \hat{x}, but how to calculate derivative respect to y? I think the last condition can be written as the following condition too:
\vert \lambda \, \frac{\partial f}{\partial x}(\bar{x}, \bar{x}) \vert < 1...
Thanks Dickfore. I owe you big time!
When you said:
You mean this system always has a fixed point?
And this point is stable if we have the last condition (which is calculated based on Jacobian matrix)?
Dear alan,
Thanks for this useful link. The link you mentioned belongs to prof. Osborne and the interesting point is that currently I'm working on game theory and my function "f", is for a dynamic game! This link seems pretty good. Really thanks.
Thank you friends. I'm following your...
Dear coelho,
Really thanks for reply.
The big problem is that this function is a function of several previous points!
For this function suppose that we have x_1 , x_2, x_3 near a and also |x_2−a|<|x_1−a|<|x_0−a| , i.e., different points are get closer and closer to the final point a. I...