What is Optimization: Definition and 627 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.
Homework Statement
An isosceles triangle has a rectangle inside of it with length 2 cm and width 6 cm. What angle ∅ will give the triangle the minimum area. Homework Equations
A =1/2 (bh)
The Attempt at a Solution
Hey guys,
1. basically I am using the silvaco athena and i got some code to make the solar cell simulation. and my project is basically about designing pn junction in terms of the solar cell.
kinda clueless of what are things that i need to modify in the code to make sure that i have a good...
Homework Statement
A(\vec{x}) = (F + T * x )2
F is a constant,
x is a 2×1 vector
T is a (constant) 1×2 matrixB(\vec{x}) = || K.Z.x ||2 k:3\times3 matrix and Z:3\times2, x the same as aboveB(x) is also R2→RC(x) = A(x) + B(x)
Homework Equations
1- I am confused...
A farmer wishes to build a rectangular chicken coop with as close to, but not greater than N square units. He wants to purchase the least amount of fencing possible, but fencing can only be purchase by the integer foot. How does he do this?
P = 2x+2y
N = xy
y=N/x
P = 2x + 2(N/x)
P' =...
Hello everyone,
This is my first post on here, I was hoping it wouldn't be asking for help but I don't have any options left and it's a problem that is due soon. I promise I have tried to solve it myself but I'm unsure if I'm doing it correctly and it is part of a take home test.
Homework...
Homework Statement
I have a whole two courseworks on Genetic Algorithms, but we have been shown no examples. I am stumped!
1. A function f is set to depend on five variables x1, . . . , x5 where x1 can take 2 different
values, x2 can take 8 different values and x3, x4, x5 each take 4 different...
Homework Statement
The printed area of a page in a book will be 81cm^2. The margins at the top and bottom of the page will each be 3cm deep. The margins at the sides of the page will each be 2cm wide. What page dimensions will minimize the amount of paper?
Homework Equations
Area=...
Homework Statement
Build a steel drum (right circular cylinder) of fixed volume V. The cost of the material is the same for the top and sides (same gage and same cost) and disregard waste. What is the relationship between the height of the radius that will minimize the surface area of the...
Hi everyone,
I am comparing the following optimization problems:
Prob Space =(Omega, F_T, (F_t)_{t=1, ..T}, P). Let X be an adapted process.
I denote E[|F_t] as the conditional expectation given F_t.
1.Z_t(omega)= max{ E[X_s | F_t](omega) : s=t, ..,T}
2. Y_t(omega)=max{E[X_tau |...
Calculus Homework Help -- Optimization Word Problem
I'm in a University Calculus class, and I am having trouble with one of my homework questions. Much help would be appreciated!
"Determine the height and radius of the cylinder of greatest volume that can be inscribed in a sphere of radius...
Homework Statement
The electrostatic potential at each point in the region 4x^2 + 9y^2 <= 36 is given by f(x,y) = 3x^2 + 2xy - y^2 + 5. Find the maximum potentials in the region.
(Without using Lagrange Multipliers).
The solution also said how to do it with Lagrange Multipliers but I...
Homework Statement
I have a sector of a circle with area 12 square meters. If radius r and angle \theta are chosen so that the that perimeter of the sector is the smallest possible, then what is the radius?
Homework Equations
I have area of sector as A=\frac{\theta r^2}{2} which is 12...
Just reviewing for a chapter test... I've always found optimization problems easy, but I don't have answers for these review questions so I thought I'd check my work on here.
Homework Statement
A piece of cardboard is 14 inches by 10 inches and you are going to cut out the corners and fold up...
Homework Statement
Homework Equations
Constrined optimzation
The Attempt at a Solution
("o" means dot product)
Let M={x|Ax=c} and f(x)=(1/2)x o Qx - b o x
Suppose x0 is a local min point.
Suppose, on the contrary, that x0 is NOT a global min point. Then there must exist a...
Dear forum,
I am new here, so hi to all!
I am using Madgraph to generate some events about exotic physics. The problem is that when I give this line
gg>(rho>(pip>j j)(pip>j j))(rho>(pip>j j)(pip>j j))
All these are declared in the particles.dat file.
The problem is that it takes too much...
Homework Statement
Hello! I'm having some difficulty getting the objective function out of this question, any help/hints would be appreciated >.<
Company A prepares to launch a new brand of tablet computers. Their strategy is to release the first batch with the initial price of p_1 dollars...
Hi There,
What's the best core loading pattern optimization method?
I believe this is very depended to experts knowledge, I mean the methods such as Genetic Algorithm or Neural Network or Ant Colony are not so useful for such these optimization.
Please correct me if I'm wrong on this.
Thanks
Hi,
I have formulated what I believe to be a generalized(to some degree) optimization under uncertainty problem. The write up is included in the attached file. I would appreciate any and all input, help or guidance as to how this problem could be solved. If you have any questions please feel...
Hi guys, me and my fellow classmate have been working on a math problem we believe to be a Modeling and Optimization type problem in our calculus class. We've been at it for 2 days now! Just can't seem to figure it out... We'd really like appreciate and all help!
Homework Statement
[There is...
hi all,
I would like to be regarded as a novice on the subject matter. I am doing a research on optimization of animal fence wire.
the idea basically is that, i want to improve on the existing design of wire used for animal fencing to minimize the chances of animals breaking out of fence...
Homework Statement
A wire 6 meters long is cut into twelve pieces, eight of one length and four of another. These pieces are welded together at right angles to form the frame of a box with a square base.
a) Where should the cuts be made to maximize the volume of the box?
b) Where should the...
Hi
I am having a lot of trouble with this problem. I don't actually know where to begin.
A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used.
Need to find:
sides of base cm
height...
Homework Statement
I have attached a picture with the problem and my attempt. The answer is D=L/sqrt(3). I know that a much easier method to solving this is by setting the distance from B to D equal to x. However I wanted a more challenging derivation and set the distance from D to C equal...
Hello there! I was decorating my Christmas tree recently, and for some strange reason, I thought: "Hrm, I wonder if I could come up with an optimization problem where I have a definite length of lights/garland, and want to have equal space between each strand of lights/garland as they go around...
Homework Statement
You are a lab technician and must create 250 ml of a 17% solution. You have availible three stock solutions. You have a one liter container of a 5% salt, a 500 l contained of a 28% salt solution, and a 400 ml container of a 40% salt solution. Show the work necessary to...
Just curious if Newton's method in high dimensions should always quickly converge to a min/max or saddle point. I can't seem to get the value of my gradient below 12-16; so, its not "diverging" but its not converging either. I want to avoid saddle points so I'm using Fletcher-Reeves method...
The manager of a department store wants to build a 600 square foot rectangular enclosure on the store's parking lot in order to display some equipment. Three sides of the enclosure will be built of redwood fencing at a cost of $7 per running foot. The fourth side will be built of cement blocks...
Hi,
I work in NRM and need for some reason to optimize an objective function of the form ||M-M_target||^2 where M is the product of a large number (>100) 2D unitary complex matrices (Qi) and a vector (A), i.e. M=Q1*Q2*...*QN*A, and M_target is a constant complex vector. I can do it directly...
A cylindrical can with height h and radius r is to be used to store vegetarian chilli. It
is to be made with 6 square centimetres of tin. Find the height h and radius r which
maximizes the volume of the can.
Hint: The volume of a cylinder is r2h and the surface area of the side walls of a...
So I have a problem. The problem says:
A fence 8 ft tall rubs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
I drew a picture to help, but I can't draw it...
Homework Statement
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3. Homework Equations
V=π*r^2*h/3
A=πr^2 + πrl
The Attempt at a Solution
I did multiple things that I'm not sure are correct. I took the derivative for the volume with the value of...
Homework Statement
what is the maximum volume of an open top box that can be created with 300m sq of metal assuming none is wasted?
Homework Equations
The Attempt at a Solution
so that means the surface area of the box must total 300 m sq
so
A(l,w,h)= lw + 2lh + 2wh = 300...
I have an optimization problem which am not able to figure out after much thought. Any suggestions on how to go about it are welcome. Thanks in advance.
given a set of 'n' numbers. I have to find the optimal disjoint subset distribution of the set which minimizes the value given by a function...
Homework Statement
I need to optimise a couple of equations.
I want maximum S for minimum x.
Constants:
h, t
Variables:
w, jHomework Equations
S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
x = (const) * (j / w) [Eqn 2]
[See attachment]
The Attempt at a Solution
Well...
I've tried to re-arrange...
I am trying to heavily optimize a piece of code in C as well as MIPS assembly. Here is a link to my code: http://dl.dropbox.com/u/7264839/P1-3.c
http://dl.dropbox.com/u/7264839/P1-4-1%20new.asm
The problem is find the number of intersections between 1 pixel wide lines of different colors...
Hi all,
I have this kind of optimization problem:
Variable to control: A=A=[a1;a2;...;am]
objective function to minimize: L=A*TL
where
L is a scalar
T is a matrix [1,m]
TL is a matrix [m,1]
constrain:
Dt>Dtv
where:
Dt=[dt1;dt2;...;dtn]
Dtv=[dtv1;dtv2;...;dtvn] is a...
Homework Statement
A real estate company owns 180 apartments, which are fully occupied when the rent is $300. The company estimates that for each $10 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the max income?
Homework...
Homework Statement
I am trying to follow along in my textbook on wireless communications (this is an Electrical Engineering course), and I am having trouble following the mathematics.
The idea is to maximize the "capacity" of a channel according to a given constraint. This involves the...
Hi all,
Hopefully this is the right section for my post, if not I apologize.
I'm hoping I can just get some advice to help me get started in the right direction. I am trying to do a mathematical inversion for the following:
\frac{1}{N(zi)} \frac{dN}{dz}|_{z=zi} = -\frac{2}{zi} -...
1) How to justify if there is a tie for the minimum b-ratio at some iteration of the phase II simplex algorithm, then the next basic feasible solution is degenerate.
I have no idea how to justify it. Please give me some direction
2) Max. z = transpose of C * the vector x
s.t...
Homework Statement
The fuel consumption of a river boat is kv3 litres per hour where k is a constant and v km/h is it's speed through the water throughout this question v > 4 km/h.
i) determine the fuel consumption for a trip of x km against a current of 4km/h and find the speed at which...
For my economics/game theory thesis I need to optimize a function subject to an inequality constraint.
maximize f(x1, x2) = 1/(x1+x2+y1+y2-w) subject to g(x1, x2) = x1+x2+y1+y2 < w
This isn't particularly important, but the x and y variables are quantity of production by a firm. The objective...
Question:
Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/5 of the maximum possible value?
Attempt:
F = [...
Homework Statement
A coffee firm sells "Premium blend" and "Economy blend" co ffee. Both are blended
from three basic grades of coffee, A, B and C:
Premium blend = 50% A + 40% B + 10% C
Economy blend = 10% A + 40% B + 50% C
The market prices are $1130/tonne for Premium and $750/tonne for...
Homework Statement
I am doing an assignment in my Linear Algebra class. But I don't know how I will go about solving this problem.
So the problem is a network of water pipes. I start with a matrix and I get the solution to the system from the RREF matrix. All the flow directions are set, so...
trying to find a global min/max while avoiding saddle points ... If we expand a polynomial of several dimensions we get the following:
f(x + del x) = f(x) + del x * g + .5 (del x) H (del x)^t + O(||x||^3) : g is the gradient, H is the Hessian.
then we can take the eigenvectors of H and...
Well, I'm having trouble doing optimization problems (maximizing and/or minimizing a function in more then one variable with/without constraints).
Would be a great help if someone could give me some good links on this topic or some methods generally.
If the domain is compact; where are the...
I have some understanding of how to solve problems involving compact domains.
Set the gradient to zero and solve for x and y, and then try to parameterize if needed to find max/min over the border of the domain.
The thing is, my book doesn't go into much detail on how to do optimize functions...