New book about optimization on manifolds

[Nicolas Boumal]

Hello everyone,

I would like to announce a new book about optimization on manifolds, now freely available online as an advanced draft:

An introduction to optimization on smooth manifolds

http://www.nicolasboumal.net/book

This is accessible to readers who are comfortable with linear algebra and multivariable calculus. There are no prerequisites in geometry or optimization.

In particular, you may be interested in:

• An introduction to Riemannian geometry for manifolds embedded in linear spaces (Chapters 3 and 5)
• Pointers on how to compute gradients (Section 4.7, also valuable for Hessians)
• An explanation of how the checkgradient and checkhessian tools in Manopt work (Sections 4.8 and 6.7)
• A study of retractions based on nonlinear projection to the manifold (Section 5.11)
• Fully worked out geometric tools for various manifolds of interest (Chapter 7)
• The link between optimization on manifolds, constrained optimization and the Lagrangian (Section 7.7)
• The mathematical foundations for Riemannian gradient descent and Riemannian trust-regions (Chapters 4 and 6)
• A detailed, pragmatic treatment of quotient manifolds (Chapter 9)
• A discussion of more advanced tools, including Lipschitz continuity on manifolds (Chapter 10)
• A primer on geodesic convexity (Chapter 11)

To a large extent, this book is a response to the many questions received through this forum and elsewhere, which illustrate the need for a primer on geometry aimed at applied mathematicians and engineers. My hope is that this new introduction, unusual in several ways, may prove a smoother entry-point for many readers.

Please feel free to share any and all feedback, as this draft can still change.

Best wishes to all, and stay safe,

Nicolas

[Arrigo Benedetti]

Awesome! Looking forward to ordering the printed edition.

[TIAN LIN]

Thank you so much ！ 

[Alberto Tono]

This is great thank  you

[TIAN LIN]

Actually, I think it is the best cookbook for a green hand like me, I really enjoy it. 

My math is not good, and I just have knowledges of basic linear algebra (as I major in communication systems).

Nevertheless, I can understand the main idea of the books, and really like the style of this book. That is, the author

used lots of simple but specific examples to illustrate the main idea of the manifold, which is of great benefit for 

readers to understand. 

Thank you Nicolas, I think every reader can enjoy this book. For me,  hopefully you can provide the solution of the exercise, 

they are very interesting but I'm not sure if I have solved it in a correct way. 

Thank you so much, also I want to write Chinese blogs of this book and recommend more people to read this book.

[TIAN LIN]

Dear Nicolas, 

long time no see,  how to cite your book? Is there some .bib formats? 

Thank you for your response in advance!

Best Wishes
Tian Lin

[Nicolas Boumal]

Hello,

The most up-to-date bibtex entry should appear on http://www.nicolasboumal.net/book.

Currently, you can use the following:

@Booklet{boumal2020intromanifolds,
  title        = {An introduction to optimization on smooth manifolds},
  author       = {Boumal, Nicolas},
  howpublished = {Available online},
  month        = {Nov},
  year         = {2020},
  url          = {http://www.nicolasboumal.net/book},
} 

Best,

Nicolas 

[Jayadev Naram]

Hello sir,
        I really enjoy reading this book. Thanks for making this book as preparation to AMS08.
I would like to point out a feature that might be helpful for the time being. It would be great

to have an update log on the book webpage to indicate the new changes in this version of 

the book. This is totally optional but would be great, to keep track of new things added. It is 

a long book to identify such changes.

Regards,

Jayadev, N.

[Nicolas Boumal]

Dear Jayadev,

Thank you for your message.

I agree that a change log could be useful; I will consider it for the next update, but I am not certain that I will have the time.

Best,

Nicolas

[Yanni Papandreou]

Dear Nicolas,

I am trying to access your book "An introduction to optimization on smooth manifolds" at the link "http://www.nicolasboumal.net/book" which does not seem to be working. Is this book available anywhere as I believe it will help me in my research?

Kind regards,

Yanni Papandreou

[Nicolas Boumal]

Dear Yanni,

Thanks for letting me know: it appears the website of my department (and my website by inclusion) is down at the moment. This shouldn't last long hopefully, but otherwise I'll come back here to post the current version of my book.

Best wishes, 

Nicolas 

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[Yanni Papandreou]

Dear Nicolas,

Thanks for getting back so quickly. I will check again tomorrow!

Best wishes,

Yanni

[Nicolas Boumal]

It appears to be back online :).

[Yanni Papandreou]

Dear Nicolas,

Thanks for letting me know!

Best wishes,

Yanni

[Nicolas Boumal]

A significant update of the book is now available here, dated Jan. 30, 2022:

http://www.nicolasboumal.net/book

Compared to the Sep. 2020 version, the writing and mathematical content was improved throughout, a small number of errors were fixed, and a few sections were added (fleshing out metric projection retractions, second fundamental forms, geodesic convexity, local convergence analyses, ...).

This version forms the basis for a forthcoming publication by Cambridge University Press.
If you spot any issues, I'd be grateful if you can let me know (there is still time to fix them).

Best wishes,

Nicolas