Introduction to Optimization

Agenda

• What is optimization?
• A method for optimizing
• Practice

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What is Optimization?

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What is Optimization?

• Finding the “best” possible result
• But “best” could mean different things to different people
• This is an extensive area of mathematics with ongoing active research
• For now, we start simply, and then grow

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What is Optimization?

• Consider the two graphs
• One has a maximum
• The other a minimum
• In both cases the extremum has derivative zero

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What is Optimization?

• What about this graph?
• There are local max/mins (extrema)
• In both cases, the derivative is zero

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What is Optimization?

• The previous graphs lead to a method (described shortly)
• We will be looking for where the first derivative of some function vanishes
• This might be an extrema
• This might solve the optimization problem we are trying to solve
• In this course, that’s mostly going to be true!

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A Method For Optimizing

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A Method for Optimizing

• Back to Polya! (recall P2 Introduction to Problem Solving)
• Understand the problem
• What are you trying to optimize?
• Can you draw a diagram?
• Define all your variables
• Make one or more functions to describe the problem
• Simplify the problem (somehow)

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A Method for Optimizing

• If you’ve done this correctly (for this course only!)
• You should have one function with one variable
• Now optimize it!
• Find the first derivative
• Use the First Derivative Test
• Where are the extrema?
• Where do they apply to your problem and does this solve your problem?

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A Method for Optimizing

• Finally, you’ve solved the problem!
• Reflect
• Is there another way?
• Are you finished?

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Practice

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Practice

• Go to the Jamboard A2 Examples Introduction to Optimization

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Credits

Special thanks to all the people who made and released these awesome resources for free:

• Presentation template by SlidesCarnival
• Photographs by Unsplash

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