<p>As in <a href="https://en.wikipedia.org/wiki/Calculus_of_variations" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Calculus_of_variations</a></p>

<blockquote>
  <p>The calculus of variations is a field of mathematical analysis that
  uses variations, which are small changes in functions and functionals,
  to find maxima and minima of functionals</p>
</blockquote>

<p>The Gradient Descent algorithm is also a method to find minima of a function, it it a part of the Calculus of Variations?</p>

CC BY-SA 4.0
2020-02-04T11:34:45.123Z
How is this question related to AI? You should at least mention where variational calculus can be used in AI. I know where it can be used, but you should edit your post to make this question more on-topic.
nbro
CC BY-SA 4.0
2020-02-04T17:32:19.343Z
Gradient Descent is AI, and the confusing term here is 'finding minima'
Dan D.
CC BY-SA 4.0
2020-02-04T22:59:49.463Z
@datdinhquoc GD alone is not AI. GD is an iterative optimization algorithm, which can also be used in other contexts that someone would not necessarily call AI. I will help you. You could say something like "GD is used to train neural networks and variational calculus is used in computer vision" as a premise, then ask your question.
nbro
CC BY-SA 4.0
2020-02-05T03:15:05.800Z
it's maths, yes, but it's used in AI as the basic optimiser
Dan D.
CC BY-SA 4.0
2021-09-25T01:59:33.957Z
@datdinhquoc ok. but this is related with Directional Derivatives and the Gradient Vector, max and min values from Calculus? anyone can confirm?
rubengavidia0x
<machine-learning><gradient-descent><variational-autoencoder><calculus><math>
Is Gradient Descent algorithm a part of Calculus of Variations?
Dan D.
# Is Gradient Descent algorithm a part of Calculus of Variations?

(Asked by: username_0 on 2020-02-04)

As in <https://en.wikipedia.org/wiki/Calculus_of_variations>

> The calculus of variations is a field of mathematical analysis that
> uses variations, which are small changes in functions and functionals,
> to find maxima and minima of functionals

The Gradient Descent algorithm is also a method to find minima of a function, it it a part of the Calculus of Variations?

**Tags:** machine-learning, gradient-descent, variational-autoencoder, calculus, math

> **Comments:**
> **username_1**: How is this question related to AI? You should at least mention where variational calculus can be used in AI. I know where it can be used, but you should edit your post to make this question more on-topic.  
> **username_0**: Gradient Descent is AI, and the confusing term here is 'finding minima'  
> **username_1**: @datdinhquoc GD alone is not AI. GD is an iterative optimization algorithm, which can also be used in other contexts that someone would not necessarily call AI. I will help you. You could say something like "GD is used to train neural networks and variational calculus is used in computer vision" as a premise, then ask your question.  
> **username_0**: it's maths, yes, but it's used in AI as the basic optimiser  
> **username_2**: @datdinhquoc ok. but this is related with Directional Derivatives and the Gradient Vector, max and min values from Calculus? anyone can confirm?  

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