- published: 01 Apr 2008
- views: 622850
In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.
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 comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.
An optimization problem can be represented in the following way:
Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Problems formulated using this technique in the fields of physics and computer vision may refer to the technique as energy minimization, speaking of the value of the function f as representing the energy of the system being modeled.
Optimization Problem #2 http://www.youtube.com/watch?v=EOJbmMB8uCQ An Optimization is Shown using Derivatives. I have posted another examples as well! For more free math videos, visit http://PatrickJMT.com
Find two numbers whose products is -16 and the sum of whose squares is a minimum. Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/optimization?utm_source=YTdescription&utm;_medium=YTdescription&utm;_campaign=YTdescription
This calculus video tutorial explains how to solve optimization problems such as the fence problem along the river, fence problem with cost, cylinder problem, volume of a box, minimum distance between two points, and the norman window problem. This video contains plenty of examples and practice problems. It's useful for high schools taking ap calculus or college students taking calculus 1. Here is a list of topics: 1. Optimization Word Problems - Technique - Maximum and Minimum Values 2. First Derivative and Critical Numbers - Horizontal Tangents 3. Constraint Equation vs Objective Function 4. Sum and Product of Two Numbers 5. Area and Perimeter Problems 6. Fence Problem - Rectangular Field of Area Along River - Maximizing Area 7. Fence Problem With 4 Pens 8. Minimizing Cost of ...
► Download your FREE Applications of Derivatives formula sheet! http://learn.kristakingmath.com/applications-of-derivatives/ ► Subscribe to my channel // http://www.youtube.com/subscription_center?add_user=TheIntegralCalc ► Check out http://www.kristakingmath.com for more math help! :D Understand one of the hardest and most common applications of derivatives, optimization and it's applications. Review the open topped box example to get a better grasp on applied optimization. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com ● ● ● CONNECT WITH KRISTA ● ● ● Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;) Math class was always so frustrating for...
Optimization Problem #3 http://www.youtube.com/watch?v=IRWuAoqeeGM Another Optimization Problem using Derivatives! For more free math videos, visit http://PatrickJMT.com Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor
Calculus Optimization Problems: 3 Simple Steps to Solve All Step 1: Get Two Equations Step 2: Plug One Equation into the Other & Simplify Step 3: Take the Derivative of this New Equation and Set Equal to Zero & Solve That's it - Done - Happy Day! ;-) This video contains a lesson and 2 step by step examples. Example 1: Optimization Overview (product and sum of 2 numbers) Example 2: Optimize the area of a pen for a dairy farmer More Optimization Examples at Calcworkshop.com 1 - Optimize the area of a geometric shape (rectangle) 2 - Optimize the volume of a geometric shape (box) 3 - Optimize the area of a corral for a rancher 4 - Optimize the shortest distance between two points and a curve 5 - Optimize the area of text on a page For more lessons and step-by-step examples on all to...
Calculus 1 Lecture 3.7: Optimization; Max/Min Application Problems
More free lessons at: http://www.khanacademy.org/video?v=MC0tq6fNRwU
Examples: Minimizing Perimeter for Fixed Area 2:25 Distance from Point to Parabola Method 1 16:45 Distance from Point to Parabola Method 2 30:14 Minimizing Hypotenuse through a point Right Triangle 35:23 At minute 23:38 I should have started some scratch work on the side so it did not look like I forgot the radical. While I verbally said I was going to focus on minimizing the inside function to simplify my work, I should not have labelled this last line as d'. I am only finding the derivative of the inside function. If you minimize the inside function, you will minimize the distance. Focusing on just the inside function for this part of the problem minimizes the difficulty. A note about the end of the first example. Closest Point...