A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l.
Find the maximum area when the combined perimiter is 8 meter.
I first try to construct the a function for the perimeter.
2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7
Next I insert this...
I have a data set of samples, and I made up some variables that filter out unwanted samples from the data set.
Say each sample has values ##\vec{x}=x_1, x_2,..., x_n##, and I know the values of ##\vec{x}## for each sample.
Also, if I sum up all of the samples, I get a value, ##Z##, which tells...
Hello everyone. I am triyng to calculate the route which takes less time to go from point A to point B in the presence of a constant flow (I. E. a simple version of Zermelo's navigation problem) using the GAMS software. However, if I put both points on a straight line and make the constant flow...
Hi, I'm making an electric longboard and trying to write an app for my phone to function as the remote. I've got a bunch of fancy Star-Trek-esque indicators on it, one of which is the pitch and roll of the deck. All the indicators have "danger zones" and turn red when they hit them, and for this...
Hi,
I have the following optimization problem. I have a list of tasks that I should be able to perform with my tools. Each tool costs a certain amount of money, and may be used to carry out a finite number of tasks. The goal is to choose an optimal set of tools in such a way that the toolset can...
1. Homework Statement
2. Homework Equations
I have yet to figure out any relevant equations, but I do believe that the constraint equation for the optimization problem is the y=64-x^6 listed above.
3. The Attempt at a Solution
I am currently trying to figure out methods to begin my...
Summary:
Some help would be greatly appreciated for finding the ideal taper and x/y dimensions of a trebuchet throwing arm to optimize strength and minimize the moment of inertia.
Long Version:
I am a high school junior currently in the process of working on an ambitious project to build a 21...
Hi, I am trying to solve a control problem where I have to minimize the fuel consumption of a vehicle:
$$J=\int_{0}^{T} L(x(t), u(t),t) + g(x(T),T)dt$$
##L(u(t),v(t))=\sum\limits_{i,j=0}^{2} K_{i,j} u(t)^i v(t)^j ## is convex (quadratic) and the term ##g(x(T),T)## is to have a constraint in the...
I have this word problem, and was wondering how I would go about creating a system of equations.
Here is the question:
Problem: You are a small forest landowner, and decide you want to sustainably harvest some of timber on your property. There are costs related to the infrastructure needed to...
Currently design of turbomachinery (impellers/turbines) is more a form of art than an engineering process. One has to guess a bunch of parameters and check if they are right in much later stages of design.
I was thinking about designing the other way: we know the initial and the final velocity...
I wouldn't be surprised if I've posted in the wrong section because in fact the reason for posting is to get help naming this problem. That being the first step to knowing where to look for a solution. Newbie to the forum so open to advice.
The problem: I have a complex histogram and a...
Hello , I am working on a project where i need to optimize a set of values before starting my algorithm, I have never used optimization before , I read some courses about it but i still have a problem formulating my problem , I need to minimize the error function( sum of squared difference )...
1. Homework Statement
Given a list of integers and a single sum value, return the first two values (parse from the left please) in order of appearance that add up to form the sum.
sum_pairs([11, 3, 7, 5], 10)
# ^--^ 3 + 7 = 10
== [3, 7]
sum_pairs([4, 3, 2, 3, 4]...
I'm trying to solve a problem that amounts to:
Given b0, ..., bn-1 where1 <= bi, find the max of |a0 - a1| + |a1 - a2| + ... + |an-2 - an-1| where 1 <= ai <= bi.
I'm 100% confident that each ai is either 1 or bi.
I'm 90% confident that the elements a0, ..., an-1 are either
1, b0, 1, b1...
Dear Physics Forum friends,
I am currently stuck with the following question about the integer optimization:
"Produce a family of 0,1 knapsack sets (having an increasing number n of variables) whose associated family of minimal covers grows exponentially with n."
My thought is that I need to...
http://tinypic.com/r/1570ojk/9
Please see the image. I don't understand how to solve such a problem. It has three criteria. Any hints or guide would be appreciated or even a solution. This is actually just an example from the book, but the book doesn't even solve the question, so I don't even...
Im trying to solve the following problem from the book 'Learning with kernels', and would really appreciate a little help.
Background information
- Let $\{(x_{1},y_{1}),...,(x_{N},y_{N})\}$ be a dataset, L a Loss function and $H(k)$ a reproducing kernel Hilbert space with kernel $k$. The...
I try to find out how to minimize functions i R by using nlm function:
> f<-function(x,y){x^2+y^2+10-5*x-y}
> nlm(f,0.1,0.1)
That only gives me an estimate for x. How would write the code to get x and y?
I have seen the implementation of L-BFGS-B by authors in Fortran and ports in several languages. I am trying to implement the algorithm on my own.
I am having difficulty grasping a few steps. Is there a worked out example using L-BFGS or L-BFGS-B ? Something similar to...
I am assigned to design a circuit that peaks voltage at 10kHz and is less than half peak voltage at 3k and 30k. Only capacitors and resistors are allowed. The circuit I'm using is attached. I end up with
##I_0 = [\frac{-R_2\omega^2C_1C_2 + [C_1+C_2]R_1R_2\omega^3C_1C_2 - R_1\omega^2[C_1+C_2]^2...
Hi,
I am trying to understand the functional form of B3LYP from the Gaussian output file. I have tried to relate the details in the output file with the functional form of B3LYP. But I am not sure what certain terms correspond to. I have mentioned below the details. Can you pleaese help me.
In...
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}...
Hi everyone,
I am new here. I am working in geophysics and I would like to invert for a simple layered velocity model using CMA-ES optimization method. I downloaded the purecmaes.m code in Matlab here: https://www.lri.fr/~hansen/cmaes_inmatlab.html, and also implemented one in Fortran 90. I...
First time posting here so excuse me if I don't know the rules so well. I figured this would be the best place to post this question.
I'm trying to optimize the force produced by a solenoid that is no bigger than 15mm in diameter (D). My goal is to get just the right balance of number of wire...
1. Homework Statement
The cylinder x^2 + y^2 = 1 intersects the plane x + z = 1 in an ellipse. Find the point on the ellipse furthest from the origin.
2. Homework Equations
$f(x) = x^2 + y^2 + z^2$
$h(x) = x^2 + y^2 = 1$
$g(x) = x + z = 1$
3. The Attempt at a Solution
$\langle 2x, 2y...
1. Homework Statement
A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a rectangle with the maximum area.
2. Homework Equations
P = 2(l+w)
A = lw
3. The Attempt at a Solution
This is what I don't understand, the solutions that I saw from...
Max: 3x + 5y
s.t. x + 2y ≤ 5
x ≤ 3
y ≤ 2
x,y ≥0
By the simplex method, the profit is $14. Using sensitivity analysis I changed the RHS of the 1st constraint and keeping everything else constant, I get the best profit value of $19 at RHS of 7.
What other methods can I use such as the...
C \in \mathbb{R}^{m \times n}, X \in \mathbb{R}^{m \times n}, W \in \mathbb{R}^{m \times k}, H \in \mathbb{R}^{n \times k}, S \in \mathbb{R}^{m \times m}, P \in \mathbb{R}^{n \times n}
##{S}## and ##{P}## are similarity matrices (symmetric).
##\lambda##, ##\alpha## and ##\beta## are...
So, I'm trying to plot a 3D "dipole" (an arrow with a small torus around it basically) in mathematica, and want to rotate it according to Euler angles...
I use this code for the rotation matrix:
rot[a, b, g] := RotationMatrix[g, {1, 0, 0}].RotationMatrix[b, {0, 1, 0}].RotationMatrix[a, {0, 0...
Hi everyone,
I am working on a mathematical optimization model for a fuel cell.
Currently I am facing a problem with the ramp-up of the cell.
I have a modulation ramp of 4% of the nominal power (58.3 kW) per minute.
My constraint in the model has to be in kWh (I have to precise that my...