Optimization Definition and 629 Threads

hello, in the task of finding the optimal phase covariant cloning machine, i have to maximize two functions of six variables :f1=a.C+b.D and f2=a.B+c.D , they are many constraints, but I've already used them to get to those expressions in the first place, the variables are real scalars and vary...

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...

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. Homework Equations $f(x) = x^2 + y^2 + z^2$ $h(x) = x^2 + y^2 = 1$ $g(x) = x + z = 1$ The Attempt at a Solution $\langle 2x, 2y, 2z \rangle...

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. Homework Equations P = 2(l+w) A = lw The Attempt at a Solution This is what I don't understand, the solutions that I saw from looking around...

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...

This is a common homework problem but.. A fence $6$ ft high runs parallel to the wall of a house of a distance of $8$ ft Find the length of the shortest ladder that extends from the ground, over the fence, to the house of $20$ ft high and the horizontal ground extends $25$ ft from the fence...

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...

A common problem with optimization of machines is that occasionally, some of the variable combinations will not be geometrically feasible. For example, if magnet angle is being parameterized in an IPMSM, it might be that at some point, the magnet skews so much that it juts out of the rotor...

Homework Statement A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below...

Hi Everyone. I am working on a model that I think can be defined as a utility optimisation problem but I'm struggling with the enunciation and notation. The model should describe how the utilities of a set of agents A={1,2,...,n} increase with the availability of a larger set of product types...

Hi. My colleagues and I are doing a research on transformers (single-phase) and we stumbled across the following equations involving hysteresis and eddy current losses: Wh = ηBmaxxfV where Wh = hysteresis losses η = Steinmetz hysteresis constant Bmax = maximum flux density x = constant...

Let F:V\rightarrow{}\mathbb{R}^{+}_{0} be a differentiable function. V is the set of all positive real-valued 2\times{}2 matrices, so V=\left\{\left[ \begin{array}{cc} a & b \\ c & d \\ \end{array}\right]\mbox{ with }a,b,c,d\in\mathbb{R}^{+}\right\} Here are the two constraints for F...

Homework Statement Find the extremizing (maximum) value of the function f(x) = sin x / x using Newton's 1D method. Homework Equations [/B]The Attempt at a Solution I know the maximum point in this equation is (0, 1). When I differentiated the equation twice and used the formula above, I...

Hey all. Let me get right to it! I have the following objective function: \mathbf{minimize} \ \ trace((G^TG)^{-1}) I am trying to minimize it with CVX. I used schur complement to do the following: \begin{equation*} \begin{aligned} & \underset{G}{\text{minimize}} & &...

I am at the moment working on a project in which I try to minimize the annual running costs of a chemical manufacturing plant. To predict annual running costs I created a model with over 50 inputs, including things such as the type of chemicals and equipment used at different points in the...

ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)] Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5. First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12...

Now I hate optimization problems and I cannot figure this one out at all. 1) A city wants to build a new section of highway to link an existing bridge with an existing highway interchange, which lies 8 miles to the east and 10 miles to the south of the bridge. The first 4 miles south of...

Homework Statement There is a typo in the problem, ”R > Σ n i=1 σi − n max 1≤i≤n σi” which should be R > n max (1≤i≤n) σi − (Σ n i=1 σi ) Homework EquationsThe Attempt at a Solution Not sure where to go with part B or where to start...

Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution...

< Mentor Note -- thread moved to HH from the technical Engineering forums, so no HH Template is shown > Okay so I'm a freshman BE student and one of our first projects is designing a windmill that can produce a voltage of 5 for 2 seconds or longer. We are having trouble find the optimal gear...

http://news.mit.edu/2015/faster-optimization-algorithm-1023 PDF: http://arxiv.org/pdf/1508.04874v1.pdf

Homework Statement Consider the ellipse ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1## that encloses the circle ##x^{2}+y^{2}=2x##. Find the values of a and b that minimize the area of the ellipse. Homework Equations ##Area=ab\pi## The Attempt at a Solution I begin by completing the square...

I ran a simulation on WinPlot (see attached video) on my computer and was a bit surprised to see that the optimal launch angle of a projectile (with NO air drag) leaving uniform circular motion is dependent on the initial tangential velocity (or at least Winplot thinks it does). Can someone...

First post on these forums, thanks all for your help! Homework Statement It is estimated that the growth rate of the fin whale population (per year) is rx(1 - x/K), where r = 0.08 is the intrinsic growth rate, K = 400,000 is the maximum sustainable population, and x is the current population...

Hello, I have data for optimization that contains different values of 4 different parameters, and the respective function value based on them. I want to find the maximum of this function, while making sure it's a "stable" maximum, i.e., for nearby parameters, the value of the function shouldn't...

Hello, Below is a description written in Latex. I am not sure how to solve this problem. I am new to linear programming and, in fact, I do not know if it can be solved by linear constraints. Please guide. Thanks

Hello, I've just finished two optimization problems for my calculus class. I would really appreciate it if someone could check my work for me. https://docs.google.com/document/d/1vcMKOg0oD0sKIrY_AzUpRrAbTsBl3nxq8vod_1dVqyE/edit?usp=sharing

Homework Statement A wire is divided into two parts. One part is shaped into a square, and the other part is shaped into a circle. Let r be the ratio of the circumference of the circle to the perimeter of the square when the sum of the areas of the square and circle is minimized. Find r...

[Moderator's note: Recategorized thread to "Basic".] While driving alone through the beautiful scenery of Banff and Yoho national parks, a question formed in my mind. Which of these modes of slowing down a vehicle by an equal amount is likely to minimize the resulting overall increase in...

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...

Warning...this requires scripting and iteration, and is not theoretical -- it is a real problem I haven't been able to solve, but I'm sure someone here can... :-) Data: each .csv file is a test recorded at a time interval of 7.5Hz and each file has 3 columns. The first column is time in...

Hello, I've been assigned two calculus problems and have completed both of them. I'm pretty sure the first one is correct but I'm iffy on the second one. I would really appreciate it someone here could check my work on the second problem, and maybe even on the first problem if they have the...

Perhaps the title says it all, but I should expand it more, I guess. So I am trying to explore more about constrained optimization. I noticed that there are very little to no formal (with examples) discussions on algorithms on nonlinear constrained optimization in the internet. They would...

Can anyone tell me straightforward information about a way to maximize a certain functional I[f]=\displaystyle\int_{X} L(f,x)dx such that the integral is bounded, T≥\displaystyle\int_{X}f(x)h(x)dx. I really know a minimal amount about functional analysis and calculus of variations, but I've...

Find the minimum of $\dfrac{1}{a-b}+\dfrac{1}{b-c}+\dfrac{1}{a-c}$ for real $a>b>c$ given $(a-b)(b-c)(a-c)=17$.

Hello again, I have a small problem. I am looking for local minimum and maximum points of the function: \[f(x,y)=3x^{2}y+y^{3}-3x^{2}-3y^{2}+2\] The first question was how many stationary points are there. I have found the derivatives by x and y: \[f_{x}=6xy-6x\] \[f_{y}=3x^{2}+3y^{2}-6y\]...

Hey everyone. I was pondering how best to optimize a chip arrangement for a poker game. This is the scenario I've thought up: There are 4 denominations of colored chips with a set value. White (W) = 0.05 Red (R) = 0.25 Blue (B) = 1.00 Green (G) = 5.00 A player wants to purchase 40 dollars...

Hello all I am trying to find minimum and maximum of the following function: \[f(x,y)=4x^{2}-y^{2}-xy-2x+6y\] under the constraints: \[y=4-2x\] \[x\geq 0\] \[y\geq -2\]I tried solving this problem using the method of the method of bounded and closed domain, understanding that the...

In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure. I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the...

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 all, I am looking for an efficient solution to solve the following problem. Can anybody help? Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite...

How can i check my solution in optimization Problems.??

Hello, This is my first post here. So I hope I'm posting in the right place, sorry if not. http://homes.soic.indiana.edu/classes/spring2012/csci/b553-hauserk/Newtons_method.pdf I am trying to solve the following numerical optimization function using Netwon's Method: So, if I have the gradient...

I am in search of (elementary) books which contains subject on the optimization problem. I'm not an electrical engineering student though so I don't know if that subject is typically taught in undergrad or grad level. But in case there is undergrad book that meets that condition, I would prefer...

1. A man is on one side of a river that is 50 m wide. He is trying to get to someone directly on the other side. There is a current flowing down the stream at 2.4 m/s. His swimming speed is 3 m/s and his walking speed is 10 m/s . What is the best angle for him to swim at to have the fastest...

Hi guys, I'm a high school senior currently in calculus and vectors. We're in our application unit right now, and I'm having quite a bit of trouble with problems that give the desired volume/area, and then ask you for the minimum dimensions required for said volume. One notable problem that I am...

Homework Statement An isosceles triangle has a base of length 4 and two sides of length 2sqrt(2). Let P be a point on the perpendicular bisector of the base. Find the location P that minimizes the sum of the distances between P and the three vertices. Homework Equations N/A The Attempt at a...

Homework Statement My question is quite specific, but I will include the entire question as laid out in the text Consider the problem of minimizing the function f(x,y) = x on the curve y^2 + x^4 -x^3 = 0 (a piriform). (a) Try using Lagrange Multipliers to solve the problem (b) Show that the...