Optimization – 1 Unconstrained Optimization
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Dear all calculus students, This is why you’re learning about optimization
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Mean Variance Portfolio Optimization I
Introduction to Optimization: What Is Optimization?
A basic introduction to the ideas behind optimization, and some examples of where it might be useful.
Hello, and welcome to Introduction to Optimization. This video provides a basic answer to the question, “What is optimization?”
In simplest terms, optimization is choosing inputs that will result in the best possible outputs, or making things the best that they can be.
This can mean a variety of things, from deciding on the most effective allocation of available resources, to producing a design with the best characteristics, to choosing control variables that will cause a system to behave as desired.
Optimization problems often involve the words maximize or minimize. Optimization is also useful when there are limits (or constraints) on the resources involved, or boundaries restricting the possible solutions.
Let’s take a look at a very simple example of an optimization problem:
Given a parabola, chose x to get the largest y.
We can try different x values to see the resulting y value. Eventually we can find the maximum y value by choosing x here. You may also have solved this type of problem in calculus class by taking the derivative of the parabola and setting it equal to zero.
Now for this simple problem it is easy to see the correct solution. For more complicated problems, it can be difficult to immediately see the correct solution, guessing and checking can take much too long, and it can be difficult to find the values where the derivative is equal to zero. To find the answers to most optimization problems we need to use a special type of program called an optimization algorithm. We’ll learn more about optimization algorithms in upcoming videos.
Optimization can be applied to a huge variety of situations and problems. For example:
Choosing the optimal location for a warehouse to minimize shipment times to potential customers.
Designing a bridge that can carry the maximum load possible for a given cost.
Choosing the optimal build order for units in a strategy game to amass the strongest possible army in a given time.
Controlling the insulin output from an artificial pancreas to minimize the difference between actual and desired blood sugar levels throughout the day.
Design an airplane wing to minimize weight while maintaining strength.
Selecting the best set of stocks to invest in to maximize returns based on predicted performance.
Temperature control of a chemical reaction
Controlling the temperature of a chemical reaction throughout a process to maximize the purity of a desired product.
As you can see, optimization is a powerful tool in many applications. This is just a small sampling of the many fields that make use of optimization techniques to improve the quality of their solutions. If something can be modeled mathematically, it can usually be optimized.
Optimization improves results by helping to choose the inputs that produce the best outputs
Most optimization problems require an optimization algorithm to solve
Optimization is applicable to many disciplines
16. Portfolio Management
MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
View the complete course: http://ocw.mit.edu/18S096F13
Instructor: Jake Xia
This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.
License: Creative Commons BYNCSA
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