Optimization theory 1: 10 minutes a day, 1 month completion

!! All optimization theory problems are expressed as multivariable functions. !!

Optimization theory is being used in a variety of fields. Let me introduce some representative fields.

AI/machine learning and data analysis, computer vision, computer graphics, applications in finance, natural sciences , etc.

Here's an important fact to know. I'll emphasize it again!!

"The fact is that all optimization problems are expressed in multivariable functional form."

If you want to approach optimization theory, the following two things are essential knowledge.

1. A precise understanding of multivariable functions

2. Exact differentiation method for multivariable functions

Many people approach optimization theory without knowing these two facts, and end up thinking it's too difficult. This lecture focuses on points 1 and 2. Once you study them, you'll eventually encounter them. Finally, I've tried to explain them simply. However, because this is a somewhat challenging field, it may not be completely easy. I recommend this lecture to anyone who is committed to consistent study and dedication. Thank you!!

Key topics covered in this lecture!

The bible of optimization theory is " S. Boyd, L. Vandenberghe: "Convex Optimization", Cambridge University Press, 2004. " It's available for download online. Once you've read this book, you'll realize how vast and profound the study of optimization theory is. This is proof that optimization theory is important and widely used. As the saying goes, "A journey of a thousand miles begins with a single step." This lecture will be your companion.

"Okay! Now, let's look at what we'll be studying."

Mathematical modeling is required to use optimization theory in this field.

A mathematical model is expressed as a multivariable function, which we call a cost function , and the method of finding the minimum of this function is called optimization.

So, studying optimization theory mathematically means

In this lecture < Optimization Theory 1>, we will study (1), (2), and (3) .

(4) Gradient descent and Lagrange multiplier method are advanced courses and will be covered in the upcoming <Optimization Theory 2>.