Improve post and add references in others

Author: duembgen

_posts/2025-08-18-blog-posts-in-2025.md

@@ -131,3 +131,19 @@ The conclusion after writing blogpost number one was: After almost a full day of
 I wish I knew how much time I actually saved by using Gemini, and if I would have found my mistake more easily had I not been in "LLM" mode with my brain. But it for sure felt like a pleasant and productive day, and I did learn a ton, not only about optimization but also about interacting with Gemini.
 
 The conclusion after writing blogpost number two is: for evolutions of the original blogpost and notebook, Gemini definitely saved me so much time. The reason is that most of the thinking and reiterating was already done with the first blogpost, and that blogpost was super useful to provide context to the second blogpost. 
+
+## Addendum: Using LLM as a reviewer
+
+In some follow-up blogposts, such as [this one](/research/2025/10/27/subspaces.html), I did not use the same pipeline but used LLMs mostly to type up my (this time, more complete) handwritten notes. However, I found it super useful to use the following prompt, which I also added to my "library of prompts" to review the post before publishing it. As attachment I simply uploaded my finalized post. 
+
+```
+I have written a blog post; see the attachment. Please provide a critique of this blog post, structured as follows:
+1. General comments
+–  Is this blog post standalone understandable by a non-expert? My target audience is graduate students and beyond with good literacy in linear algebra and optimization. If not, suggest a few concrete, concise additions that would make the blog post more understandable, in Jekyll Markdown format. 
+2. List of typos 
+– Provide a concise list of obvious typos and English mistakes
+3. English improvements
+– Suggest any edits in terms of language, keeping the same tone as the original blog post, but making it easier to read. 
+```
+
+I didn't integrate most of what was suggested under point 3, since I found it unnecessary (maybe this is due to my own ignorance, but I prefer to keep my tone unless I am convinced the proposed solution is better). But under points 1 and 2 it suggested valuable additions and spotted non-trivial mistakes! 

_posts/2025-08-18-kernel-image-primal-dual.md

@@ -5,7 +5,9 @@ date: 2025-08-18
 categories: [research]
 ---
 
-_I finally got around to writing my first blogpost, thanks to LLMs. This blogpost is not just AI-generated, but thanks to the latest and greatest LLM magic, the time to go from handwritten notes to a polished blogpost was greatly reduced. For full transparency, and maybe because others might find this interesting, I am writing [another blogpost](/misc/2025/08/18/blog-posts-in-2025.html) about my process to generated this blogpost (and hopefully a few more in the future) using Gemini. 
+_Note from November 3rd 2025: The concepts of this blogpost are better described in the [more recent post](/research/2025/10/27/subspaces.html)_
+
+_I finally got around to writing my first blogpost, and it was partly thanks to LLMs. This blogpost is not just AI-generated, but thanks to the latest and greatest LLM magic, the time to go from handwritten notes to a polished blogpost was greatly reduced. For full transparency, and because others might find this interesting, I am writing [another blogpost](/misc/2025/08/18/blog-posts-in-2025.html) about my process to generated this blogpost (and hopefully a few more in the future) using Gemini. 
 If you are interested in the follow-up question: tackling minimization rather than feasibility problems with SOS, you might want to look at [this follow-up post](/research/2025/08/24/kipd-minimization.html)_
 
 Checking if a polynomial is non-negative is a fundamental problem that appears in many areas of engineering and mathematics. While checking for non-negativity is computationally hard in general, a powerful sufficient condition is to check if the polynomial can be written as a sum of squares (SOS) of other polynomials. This condition is not only tractable—it can be checked by solving a semidefinite program (SDP)—but it is also a key component in a wide range of optimization methods for polynomial systems.

_posts/2025-08-24-kipd-minimization.md

@@ -5,6 +5,8 @@ date: 2025-08-24
 categories: [research]
 ---
 
+_Note from November 3rd 2025: The concepts of this blogpost are better described in the [more recent post](/research/2025/10/27/subspaces.html)_
+
 _This is a follow-up to my [previous post](/research/2025/08/18/kernel-image-primal-dual.html) on different formulations (Kernel, Image, Primal, Dual) of Sum-of-Squares (SOS) feasibility problems. This post took significantly less time to write because it is really an evolution of the previous post, which Gemini is amazingly good at. I added a paragraph about this in [other post](/misc/2025/08/18/blog-posts-in-2025.html) about writing blog-posts with the helpf of Gemini_