What is Optimisation: Definition and 72 Discussions
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.
The assignment is to find the optimal operating temperature and maximum product concentration of reactant B, assuming a constant temperature across the PFR length. Please could someone help? thanks
the reaction is a series reaction: A → B → C (liquid phase)
Here is my current code which is...
I try to proof it but i got stuck right here, i want your opinions
Can I get a solution if i continue by this way? or Do I have to take another? and if it is so, what would yo do?
Hello!
I am new here, and I need (urgent) help regarding the following question:
Let $\boldsymbol{A}_{(n\times n)}=[a_{ij}]$ be a square matrix such that the sum of each row is 1 and $a_{ij}\ge0$$(i=1,2,\dots,n~\text{and}~j=1,2,\dots,n)$ are unknown. Suppose that...
Dear experts,
What software is available (free or not) to optimise the member cross-sections of trusses or frames?
Which one is your favorite?
Would any of them optimise the topology and geometry?
Ideally, the global buckling of the whole structure as well as the buckling and strength of...
I got something i want to do for fun and help out a...person i know but i never finished high school so that's my degree level. i was wondering if there is a way under $100 to possibly use my internet or posibly 2 peoples internet connections on the other side of the town i live in, split up the...
Firstly, I'm not even sure how to frame this mathematically, but I'd be curious to know what kind of problem it is and what kind of subjects within maths it requires to be able to solve it.
Here's my problem--
I've set it up in excel to help you visualise it.
There is a different amount of...
I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together.
The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...
Homework Statement
A manufacturer makes a batch of n items with the cost (in dollars) of each item being:
n2-6n+35.
The manufacturer sells the items for $50 each. How many items should be produced in each batch to maximise profit.
Homework Equations
Cost = C(n) = n2-6n+35
Revenue = R(n) = 50n...
Homework Statement
A box is given with a L = 1.414w and W = w and a cut size = x. Find the general formula for the maximum volume.
Homework Equations
L = 1.414w - 2x
W = w - 2x
H = x
The Attempt at a Solution
V = x(1.414w - 2x)(w - 2x)
V = 4x3 - 4.818x2w + 1.414w2
Apparently this isn't the...
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...
I wasn't sure into which category I should post this, so feel free to move it into a more appropriate place.
As part of my work I'm solving a system of nonlinear equations, of a usual form:
$$\vec{F}(\vec{X})=\begin{pmatrix}F_1(X_1, X_2, \cdots X_N) \\ F_2(\cdots) \\ \vdots \\...
Hello everyone,I have a short question about the PSO since I am a new comer to this field. how can we "add" position with velocity in the simple PSO algorithm, when they are of different units?
I have had this problem that I didn't know how to write it properly in this thread.
Let's say I have two objective functions:
minimize X
minimize Y
Let's say I want 1. as main objective and 2. a sub objective - by that I mean if there is a set of optimal solutions for 1., then final solution...
Okay, so I've run into a rather weird functional that I am trying to optimize using calculus of variations. It is a functional of three functions of a single variable, with a constraint, but I can't figure out how to set up the Euler-Lagrange equation. The functional in question is (sorry it's...
Homework Statement
Find all stationary points of the function
G(x, y) = (x^3)*e^(−x^2−y^2)
Homework Equations
fx=0 and fy=0
The Attempt at a Solution
Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4)
Gx = 0 implies 3x^2-2x^4=0
x^2(3-2x^2)=0
hence x =0 ,+or-...
Hi there everyone, wonder if anyone can help as I'm a bit confused.
Ive been asked to find the global extreme point of f(x)=e^(x-1) - x.
I have checked my answer against the solution and am correct and my working is as follows:
f'(x) = e^(x-1) - 1 = 0. Therefore (x-1)=ln1 (which = 0) therefore x...
I am taking a course on linear regression online and it talks about the sum of square difference cost function and one of the points it makes is that the cost function is always convex i.e. it has only one optima.
Now, reading a bit more it seems that non-linear functions tend to give rise to...
Hi, I have the following equation:
f(z)=g(z)+b*u(z)
where z=(x,y) i.e. bivariate,b is a parameter, u(z) the uniform distribution and g(z) a function that represents distance.
By considering for a momment b=0, min(f(z)) can give me the location of the minimum distance. However because I want...
Hi everyone, I need a little bit of help with an optimization problem and finding the critical numbers. The question is a follows:
Question:
Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula:
V = 999.87 −...
Hi everyone,
I am a High School student (final year) and am doing an extra-curricular project. Having complete autonomy on what we do the project on, I choose to design a High-Altitude Long-Endurance (HALE) UAV, such as the QinetiQ Zephyr [http://www.airforce-technology.com/projects/zephyr/] or...
Hi everyone,
I will be taking a summer course on Optimisation - AMSI Summer School
and was wondering if you could recommend any books.
The course outline is:
Week 1: Introduction to Optimization problems: classification and examples. Elements of convex analysis: convex sets and convex...
Homework Statement
a cylindrical tin can with volume 0.3l is being made, with the top and bottom sufaces twice the thickness as the sides.
Show that a height to radius ration of h=4r will minimise the amount of aluminium required.
Homework Equations
V=\pi r^2 h \\
A = 2 \pi r^2 + 2 \pi r h...
Hi all. I have a rather unique problem that I need help with and I really didn't know how to title it.
Consider the following:
You are trying to build a factory that produces the greatest amount of goods under a given time.
You start off with a construction capacity of 20 per hour and you can...
Suppose that a firm in perfect competitive markets has the following production function:
1 1
Q = f (K,L) = K^(1/3)*L^(1/3) ,
where Q,K and L denote the production level, capital inputs and labour inputs.
The firm's cost function is given by
TC = r*K + w*L ,
where r is the costs of using each...
This is a problem I got from my friend. I think this can be solved linear algebra. Please help me to transform this problem to mathematical equations at least.
Raju has an exam after 1 month , and daily he allots 4 hours for study. He has 3 subjects to study (A, B and C) for the exam. Subject...
Hi, I am designing a plastic recycler and I need advice on choosing gauge of some nichrome wire. I want the heater to reach around 220 degrees C and I will be powering it with a laptop charger (19v 7.1 amps). Temperature control will be achieved with a PID controller.
The nichrome wire will...
Homework Statement
The problem asks to design a cantilever beam of a minimum weight consisting of 2 steps.
Given: total length (L), Force (F) at the end of the beam and allowable stress (σ)
Need to find the diameters D and d, the length of the smaller shoulder of the beam (x)...
esign a cantilever beam of minimum weight (volume) consisting of
three steps that meets condition of strength. Given parameters are: total length of the beam
L, force F at the end of the beam, and allowable stresses [sigma].
Parametres to be determined:
Beam Diameters d1 d2 d3
Length x1...
S=8x2ln(1/2x)
Find the value of x that gives a maximum.
So far I have got, by differentiating: x2+ln(1/2x). [could be wrong]
Btw the way in the question x is a ratio and so cannot equal zero.
Please help and explain how to do it thanks :)
No this is not homework.
http://imgur.com/zAZxmuC
http://imgur.com/zAZxmuC
Ok i am struggling to even start this question.
I see it has a constraint so i would be tempted to use Lagrangian but from there i don't see how px and qy fit into it?
Some assistance on the tools needed to...
Hi,
So f(x,y) = xe-x(y2 - 4y)
Find all stationary points and classify them i got
for fx(x,y) s.p (1,4),(1,0)
for fy (x,y) s.p (0,2)
I thought that you don't need double differentials at this stage and if it is a s.p it must satisfy
for fx(x0,y0) = 0
for fy (x0,y0) = 0
which...
Homework Statement
I have 12m2 of cardboard. I must make a rectangular box with no lid, but I must maximize the potential volume of the box. The length, width and height of the box are x,y,z.Homework Equations
I know that xyz = V (volume). I know the surface area is 12m2
∴ 2xz+2yz+xy=12...
Homework Statement
This is the problem that I have , but I do not have any idea..
Please help me :) and sorry if it is not in the right category.
Homework Equations
The Attempt at a Solution
Homework Statement
REFER TO IMAGE
Homework Equations
SEE ABOVE
The Attempt at a Solution
I haven't been able to start this question. I'm wondering how to find the 'average cost per unit'.
I have a university coursework where I have to optimise the mass/volume of a bike frame using the cross-sectional area & tube thickness of the cylindrical tubing. I'm fairly competent in doing this process in ANSYS workbench (at least I'd like to think I am!).
If I had the choice, I would use...
I'm looking to do a course on Optimisation, however there was no prescribed textbook and I'm a bit wary of doing a course without a textbook to reference. There was a generalised list given, of like 10 textbooks, but this is a bit too much, especially with 3 other subjects to do!
Here is the...
Homework Statement
The temperature of a point on a unit sphere, centered at the origin, is given by
T(x,y,y)=xy+yz
Homework Equations
I know that the equation of a unit sphere is x^2+y^2+x^2=1, which will be the constraint.
The Attempt at a Solution
The partial derivatives of T are...
Hi everyone,
I realize this is only loosely related to mathematics, but I didn't know where else to ask this question (if I post it in a finance forum I'll get 100 different answers from people who probably didn't really understand the question). I think mathematicians are the kind of people...
Homework Statement
A square-based rectangular prism has a total surface area of 54cm^2. Determine the side lengths if the volume is a maximum and hence find the volume.
I have done a number of these and I am getting really annoyed because I always get all the sides being equal no matter...
I am a bit confused as to how to formulate the robust optimisation counterpart for the following problem,
Homework Statement
Consider the random linear constraint Ʃj ( ~aijxj ) ≤ bi, where ~aij's are the random parameters,
Assume ~aij belongs to the uncertainty interval [aij-aij*, aij +...
Homework Statement
I initially had to use the attached diagram to solve problems related to a concert venue.So I created a formula for perimeter and area and used these to create a formula for area with x as the only variable.I used differentiation to find the value of x when the area is at...
Hi everyone,
First of all I am not sure if I have chosen the right category for this posting but this looked the most reasonable out.
I have a problem that I would like to solve but I am not sure where to look for answers. It seems like something other people might have worked with before...
Dear All
Firstly thank you for looking at my post. I am trying to nonlinearly warp an image with respect to another using a free form deformation. I am trying to code the following paper in matlab:
http://www.cs.jhu.edu/~cis/cista/746/papers/RueckertFreeFormBreastMRI.pdf
I understand...
Homework Statement
An enemy fighter jet has invaded friendly airspace and is traveling on a bearing of 40 degrees. At the time they scramble an interceptor from a nearby airbase, the enemy jet is 200km away and on a bearing of 10 degrees from the airbase. The enemy jet is traveling at...
Q. You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 130 cm3, what values of h and r will minimise the total surface area (including the top and bottom faces)?
Volume(Cylinder) = pi(r)2*h
130 = pi(r)2*h...
Hi,
I need to design a balsa bridge that will cover a distance of 200mm. It will be loaded centrally for testing. The objective of this however is not to test until failure, but to have it fail at a certain weight. Points are also given for high strength to weight ratios and simplicity of the...
Homework Statement
Consider the intersection of two surfaces: an elliptic paraboloid
z = x2 + 2x + 4y2 and a right circular cylinder x2 + y2 = 1. Use Lagrange multipliers to find
the highest and lowest points on the curve of intersection
The Attempt at a Solution
L = x^2 + 2x + 4y^2...
URGENT - optimisation problem
Homework Statement
Find the point on the line y=4x+7 that is closest to the origin.
Homework Equations
The Attempt at a Solution
I am completely lost on where to start and what to minimise. It's for exam preparation!