optimization Definition and Topics - 55 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.

View More On Wikipedia.org
  1. person123

    I Fitting Data to Grafted Distribution

    I have a set of data (representing the strength distribution of samples), and I would like to fit a normal-Weibull grafted distribution. To the left of a specified graft point, the distribution is Weibull, and to the right it's normal. At the graft point, the value and the first derivative are...
  2. Quantum computing & chill

    Quantum computing & chill

    A thing doing its own thingy thing could compute faster than a computer can compute.
  3. Mathman2013

    Optimization problem (Max area of a combined semi circle and a square)

    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...
  4. F

    Can someone recommend an algorithm to optimize this data

    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...
  5. F

    Moving a particle from point A to B on a efficient way in GAMS

    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...
  6. CK_KoopaTroopa

    I Finding the max angle of a longboard deck before the wheels slip

    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...
  7. C

    A Combinatorial optimization problem

    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...
  8. Guy Fieri

    Issue With Optimization Problem

    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...
  9. Brandon Preble

    Trebuchet Throwing Arm 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...
  10. synMehdi

    A Pontryagin minimum principle with control constraints

    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...
  11. R

    Creating system of equations from word problem optimization

    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...
  12. kandelabr

    Trajectory with minimum acceleration

    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...
  13. M

    A Summing simple histograms to recreate a more complex one

    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...
  14. Jamison Lahman

    Comp Sci Algorithm Optimization [Python]

    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]...
  15. S

    C/++/# Counterexamples to my claim?

    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...
  16. B

    Producing a Family of 0,1 Knapsack Sets

    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...
  17. T

    Multi-criteria optimization. How to solve it?

    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...
  18. E

    Sparsity of Support vector machines over an RKHS

    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...
  19. T

    How to use nlm function in R

    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?
  20. C

    Is there a worked-out example of L-BFGS / L-BFGS-B?

    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...
  21. BiGyElLoWhAt

    Optimization Problem with an RC BP filter

    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...
  22. D

    A Gaussian 09 Output file_DFT Calcuation

    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...
  23. S

    A Can this optimization problem be solved?

    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}...
  24. Kefeng

    Question about CMA-ES step size sigma

    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...
  25. Alex Sieber

    Solenoid Optimization

    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...
  26. a255c

    Lagrange optimization: cylinder and plane intersects,

    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...
  27. I

    Explain why this is correct (Optimization Problem)

    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...
  28. B

    List of quantitative methods for optimization

    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...
  29. kevin2016

    A What is the closed-form solution using ALS algorithm to optimize

    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...
  30. Mr. Rho

    Mathematica Rotation of 3D Plot using Euler angles

    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...