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.

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  1. T

    Solving Surface Optimization Problem w/Calculus of Variations

    Ok, so here's the problem: Two circular wire hoops of radius R are spaced a distance 2\ell apart. Consider a soap film stretching beatween the two hoops. Due to surface tension the film's equlibrium form is a surface of minimal area. Use the calculus of variations to find this minimal...
  2. M

    Minimizing Total Area: Optimal Dimensions for Triangles and Squares

    I was wondering if someone could workout this problem... The sum of the perimeters of an equilateral triangle and square is 10. Find the dimensions of the triangle and the square that produce a minimum total area. Thanks for any help
  3. P

    MATLAB Writing Optimization Code in Matlab - Resource Guide

    OK, here is the situation. I am supposed to write optimization code in Matlab to determine which of two missions an airplane should perform. There are three total, but one of them has been decided on. So I need to determine which of the other two I should do. The problem is that I have...
  4. V

    Optimization - maximize the sum of distances to the power alpha

    hi, what i am trying to do is maximize the sum of distances to the power alpha between all the points D_{\alpha} (\mathcal{U}) = \sum_{i=1}^m \sum_{\substack{j=1\\j\neq i}}^m|\mathbf{u}_i - \mathbf{u}_j|^\alpha on the surface of a sphere of radius 1 where \mathbf{u} \in \mathbb{R}^3 and...
  5. J

    Need help on another optimization problem

    Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If the sheet of material measures 14 inches by 9 inches, find the dimension x which represents the length of one side of the square that should be cut off so that...
  6. J

    How to Determine the Optimal Dimensions of a Tin Box to Minimize Material Use?

    Minimizing Construction Costs: If an open box has a square base and a volume of 108 in.^3, and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. This is what I have so far: Volume: 4y^3-4xy^2+x^2y=1=108...
  7. S

    Sum of two nonnegative numbers optimization

    The sum of two nonnegative numbers is 20. Find the numbers if a. the sum of their squares is as large as possible; as small as possible b. one number plus the square root of the other is as large as possible; as small as possible. a. x+y = 20 x^2 +y^2 = N (20-y)^2 + y^2 = N -40 +...
  8. E

    Cylinder vs Rectangular Prism: Which is More Economical for Juice Packaging?

    I have a really tough question and need like emergency help and aid... a juice manufacturer is studying the most economical shape to use for a beverage container. Each unit will contain 335cm^3 of juice. The manufacturer is considering a cylinder versus a rectangular prism with a comfortable...
  9. C

    Optimization find radius problem

    optimization problem! OKOK running out of time! CAn anyone please help me with this problem: Surface Area A solid os formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radiusof the cylinder that...
  10. D

    How Do I Solve These Grade 12 Calculus Optimization Problems?

    I have couple of questions on optimization, i don't want the answer, i just want to know what i have to do to approach this question. Keep in mind that I am in grade 12 calculus, i.e. PLEASE don't give me some crazy university answer with equations I've never seen before. Anyways, here are the...
  11. T

    Optimization and maximum area of a rectangular enclosure

    I've used differentiation to find that a rectangular enclosure made up of a 100m fence should have four sides all 25m to be as large as possible. The function I get is 50x-x^2. As I said, differentiating this function gives me the largest area possible. But how would I go about finding how long...
  12. E

    Optimization Problems (So confusing) Please me on this once. Thanks in a million

    Optimization Problems (So confusing) Please me on this once. Thanks in a million ! The Dome Tent 1 .Imagine making a tent in the shape of a spherical cap (a sphere with lower portion sliced away by a plane). Assume we want the volume to be 2.2 m^3, to sleep two or three people. a. make a...
  13. M

    Optimizing Costs for Enclosing a Botanical Garden with Shrubs and Fencing

    a landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the fourth side. Find the minimum total cost. I started off this problem by finding the length...
  14. M

    Optimization Problem: Minimizing an Objective Function with a Constraint

    Help -- Optimization Problem Hello people, I am working on certain energy optimization problems in multiprocessor systems. My objective function is: E= U*x / (1-yC)^2 where U and C are constants and x and y are independent variables. I need to minimize this function under the constrain...
  15. S

    Multivariable Optimization Problem

    I have two questions. A) Show the parallelipided with fixed surface area and maximum volume is a cube. I've already proven that we can narrow down the proof to a box. So, basically, I'm really lost on how do prove that a cube is the box with a fixed surface area and maximum volume. B)...
  16. R

    Optimize Positive Number Sum of Number & Reciprocal

    How to find a positive number such that the sum of the number and its reciprocal is as small as possible ?
  17. D

    Optimizing Chocolate Packaging with Equilateral Triangular Prisms

    A choclate manufacturer uses an equilateral trianglular prism package. if the volume of chocklate to be contained in the package is 400 cm ^3 . what dimenesions of the package will use the minumum amount of materials? i'm having trouble putting the formulas together, I am thinking of the...
  18. C

    Lake Walk Optimization Problem

    A woman at a point A on the shore of a circular lake with a radius of 2 miles wants to arrive at the point C opposite A on the other side of the lake in the shortest possible time. She can walk at a rate of 4 miles an hour and row a boat at 2 miles an hour. How should she proceed...
  19. M

    MATLAB Optimization: Wots wrong with my MATLAB CODE

    Optimization: I am going insane here :cry: :cry: I've really run out of ideas... please help me.! %golden.m function [f,a]=golden(func,p,tol) func='dfunc'; p=[0 1] g=0.38; a=p(1); b=p(2); r=b-a tol=0.01; iter=0 while r>tol x=[a+g*r b-g*r] y=feval(func,x) if...
  20. P

    Optimization Race Track Problem

    Hi, I just needed help starting off this problem: "A 1-km racetrack is to be built with two straight sides and semicricles at the ends. Find the dimensions of the track that encloses the maximum area." There was a similar question which I did before this which involved a Norman...
  21. P

    Where Can I Learn Online Optimization Techniques for Calculus Problems?

    is there a good website on how to do optimization online?? we learning this section now in our calc class but our teacher didn't really explain anything, he only did one example and told us the rest were all similar but i din't know where to even begin on some of then... #2. A company must...
  22. M

    Cost-effective design for fencing and partitioning a rectangular ranch field?

    hi i have two homework assignment I'm kinda stuck on they are very similar i was hoping someone could help me... 1) A rancher wants to fence in an area of 1,900,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the...
  23. J

    I'm haveing optimization problems

    This is homework (forgive me) but I don’t want an answer I would just like to know what I am doing wrong. Here is the problem: Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3cm and 4cm if tow dies of the rectangle lie along the legs...
  24. M

    Spherical Optimization and beyond

    I have a semi-project due tommorrow that basically asks the following question: If you are designing a tent in the shape of a spherical cap (a sphere with the lower portion sliced away by a plane) and the material used for the roof costs 2.5 times more per square foot than the material used for...
  25. tandoorichicken

    Find Largest Rectangle on y=12-x^2

    Find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12-x^2
  26. T

    What Is the Area of the Largest Rectangle Inscribed in a Semicircle?

    What is the area of the largest rectangle that can be inscribes indiside a semicircle with the radius r? answer: x = r / SQRT(2) A = r^2
  27. I

    Optimization Using Differentiation

    [SOLVED] Optimization Using Differentiation I have an assignment in which we are to optimize problems using a given 6-step process. More or less it involves Max/Min differentiation. On of the problems are as follow; Enclosing the Largest Area The owner of the Rancho Los Feliz has 3000 yd...
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