Optimization Definition and 588 Threads

Hi everyone, I am working on matrix inversion and focusing on low-complexity method such as iterative method. Recently, I am interested to explore how particle swarm optimization (PSO) can be applied to do matrix inversion. Since I am very very new in PSO, I have no idea how to start my work...

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...

Homework Statement A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence What should the dimensions of the garden be if the area is...

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 guys, i am preparing my self for the calculus 1 2 3 final and i need recommendation about optimization problems theories book or something to help me understand how to solve and understand optimization problems and to solve them. Thanks♥

Homework Statement I would like to solve for Y an optimisation problem Homework Equations Max Y'C + Y'Br + αr0 Subject to : k=sqrt(Y'ΣY) Y'e + α = 1 Where Y, C and B are columns vector of n lines. Σ is symetric matrix of n order e =(1,...1)' and α is a reel parameter. I did calculus with...

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...

Homework Statement 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. The Attempt at a Solution I am currently trying to figure out methods to begin my optimization...

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...

I have a system of equations which I solved with Newtons method. Call Newtons method a function NM=f(K1,K2). K1 and K2 are input and a vector of x=x1,x2,x3,x4 is output. I have another function, SSR, the sum of square residuals. It looks like this : $$\sum...

The gains of an OP-AMP are listed below: G_d = (R_1*R_4+R_2*R_3+2*R_2*R_4)/(2*R_1*(R_3+R_4)) G_s = (R_1*R_4-R_2*R_3)/(R_1*(R_3+R_4)) \frac {\partial G_d} {\partial R_1} = -R_2*(R_3+2*R_4)/(2*R_1^2*(R_3+R_4)) My questions is... Is there a mathematical perform the following: Differential gain...

Can someone please tell me how to go about optimizing this system of equations? It is weird because the residuals are computed with ##A = B*X_1+C*X_2## but X_1 and X_2 are computed in a separate function ##[X_1,X_2]=f(k1,k2,H0,G0)##, and what I am optimizing is a parameter in that second...

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...

Homework Statement This is a leetcode question. You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security system connected and it will...

I wonder what is the best figures for blades/prepellers - assuming I am trying to optimize battery life and my main usage for the drone is hoovering. I can not play with the arm length. I do consider 4 blades over 2 blades at the same propeller - not sure if it will help. Any feedback or idea is...

I am little confused when it comes to optimization problems. For example, say we are given that ##x+y=2##, and are asked to maximize ##xy##. By AM-GM, we have that ##xy \le 1##. But why should this indicate that ##1## is the maximum value? Isn't it an equally true statement to claim that ##xy...

Homework Statement For positive x, y, z where ##x \le y \le z## such that x + y + z = 3, what is the maximum value of ##xy##? Homework EquationsThe Attempt at a Solution First, before I attempt a solution, isn't it the case that ##x=y=z=1##, since the only partition of 3 into three terms is...

Hi, I may have discovered a textbook error but I'm no calc whiz. I need an assist to find out if the question unintentionally described a square instead of a rectangle. I have attached the textbooks solution as well as my attempt at a solution. The numbers check out, I just want to make sure...

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...

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...

Homework Statement Find any maxima/minima on f(x,y) = x2+2y2 on the unit circle, centered at the origin. Homework Equations grad f = λgrad g constraint: 1=x2+y2 The Attempt at a Solution grad f = 2xi+4yj grad g = 2xi+2yj 2x=λ2x 2y=λ4y How do I solve this? I don't see any way to get numbers...

I am a city kid with a windowsill with the dimensions 12x5 inches. I have peas which require a 1x4 space and make me 15 dollars, and carrots which require 1x5 space and make me 50. I can only make 15 sets of peas if I were to use the whole space, and 12 sets of carrots if I were to use the whole...

Hi, I'm a Civil Engineering student doing my final project for my BE degree. I have developed a software that uses a genetic algorithm for optimizing reinforced concrete columns. I have tested my program with a 17 stories building, and got some very unusual results in the design but much...

Hello all, I'm a Mechanical engineer with no prior experience in designing flow systems. I'm struggling with a hydraulic system that I have to design. the number of unknowns is large. but maybe by dividing the system to small sections, a solution can be found. I attached a schematic drawing...

Hey! :o To product a product $3$ square plates $A$ with measures $300\times 500$mm and $2$ square plates $B$ with measures $400\times 600$mm are needed. These plates must be cut out by two different workpieces with measres $1000\times 1000$mm (Type I) and $600\times 1500$mm (Type II). The...

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...

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...

Here all, Here's a problem I'm trying to solve. Given a planar piecewise linear and circular curve (ie. a curve consisting of line and circular arc segments) that represents the path of a particle; a set of rules for traversing the two types of curve segments as well as the transitions between...

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...

Problem: Fix some vector ##\vec{a} \in R^n \setminus \vec{0}## and define ##f( \vec{x} ) = \vec{a} \cdot \vec{x}##. Give an expression for the maximum of ##f(\vec{x})## subject to ##||\vec{x}||_2 = 1##. My work: Seems like a lagrange multiplier problem. I have ##\mathcal{L}(\vec{x},\lambda)...

Dear Forum, I am working on projectile motion and optimization these days. Projectile motion uses the kinematic equations of free fall for the vertical direction together with the equations of constant velocity in the horizontal direction. Maximum Range: if an object is launched at a certain...

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}...

I have a program that searches out string types.. Here is what I have so far - C# language. if(word.Contains "Hello") {...} else if(word.Contains "Bye") {...} else if(word.Contains "Yes") {...} ... I plan to add more and more of those if statements as my program advances. Would organizing...

A student wishes to minimize the time required to gain a given expected average grade, 𝑚, in her end-of-semester examinations. Let $${t}_{i}$$ be the time spent studying subject i$$\in$${1,2}. Suppose that the expected grade functions are $${g}_{1}$$($${t}_{1}$$) = 40+8$$\sqrt{{t}_{i}}$$ and...

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...

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...