Longest Path Searchhttps://guille.site/Wed, 16 May 2018 00:00:00 -0700PCA as a convex optimization problemhttps://guille.site/pca-convex.html<p>It's been a while since I last posted (my posting has been less once every two weeks and more like one every two months), but here's a post I've been sitting on for a while that I never got around to finishing. As per <a href="https://rachelbythebay.com/w/2018/03/13/write/">rachelbythebay's advice</a>, I decided to just …</p>Guillermo AngerisWed, 16 May 2018 00:00:00 -0700tag:guille.site,2018-05-16:/pca-convex.htmlmathpcanon-convexconvexFast shortest paths for time-varying graphs (Part 4/?)https://guille.site/path-optimization-thoughts4.html<p>This is the fourth post in a series of posts describing an approach to doing path-planning in real-time on a small, embedded compute board. This is yet another relatively standalone post which mostly describes how to generate a (starting) path used in the <a href="/path-optimization-thoughts2.html">second</a> and <a href="/path-optimization-thoughts.html">first</a> posts to generate a …</p>Guillermo AngerisSat, 17 Mar 2018 00:00:00 -0700tag:guille.site,2018-03-17:/path-optimization-thoughts4.htmlcontrol-theorymathnon-convexpath-planninggraph-theoryauvsiComparing continuous optimization heuristics vs. reinforcement learning (Part 3/?)https://guille.site/path-optimization-thoughts3.html<p>This is the third post in a series of posts describing an approach to doing path-planning in real-time on a small, embedded compute board. Though this one is more of a standalone post (e.g. doesn't really require much reading of the previous), it compares the performance of the algorithms …</p>Guillermo AngerisMon, 25 Dec 2017 00:00:00 -0800tag:guille.site,2017-12-25:/path-optimization-thoughts3.htmlcontrol-theorymathnon-convexpath-planningreinforcement-learningdnnauvsiProximal gradient for SVMhttps://guille.site/svm-prox.html<p>For a class that's currently being written (<em>ahem</em>, EE104), Prof. Boyd posed an interesting problem of writing a (relatively general, but ideally simple) proximal-gradient optimizer. The idea is that would act as a black-box way for students to plug in machine learning models of a specific form and have the …</p>Guillermo AngerisFri, 22 Dec 2017 00:00:00 -0800tag:guille.site,2017-12-22:/svm-prox.htmlmachine-learningmathoptimization-methodsOptimizers, momentum, and cooling schedules (Part 2/?)https://guille.site/path-optimization-thoughts2.html<p>This is the second post in a series of posts describing an initial approach to doing path-planning in real-time on a small, embedded compute board. For the first in the series which describes the energy function used below, see the <a href="/path-optimization-thoughts.html">first post</a>.</p>
<h2>Quick recap</h2>
<p>Anyways, we left off on the …</p>Guillermo AngerisSun, 22 Oct 2017 00:00:00 -0700tag:guille.site,2017-10-22:/path-optimization-thoughts2.htmlcontrol-theorymathnon-convexpath-planningauvsiSome thoughts on global path optimization (Part 1/?)https://guille.site/path-optimization-thoughts.html<p>I usually see path planning in some shape or form usually solved as a Bellman update, Dynamic Programming-style problem, where the given control is asymptotically stable and optimal; in general, this seems to work quite well, but when we have so much computational power available now-a-days, I do wonder if …</p>Guillermo AngerisTue, 17 Oct 2017 00:00:00 -0700tag:guille.site,2017-10-17:/path-optimization-thoughts.htmlcontrol-theorymathnon-convexpath-planningauvsiLeast-squares and image processinghttps://guille.site/ls-images.html<p>Least squares is one of those things that seems relatively simple once you first look at it (perhaps also because most linear algebra texts relegate it to nothing more than a page or two on their textbooks), but has surprisingly powerful implications that are quite nice, and, most importantly, that …</p>Guillermo AngerisTue, 19 Sep 2017 00:00:00 -0700tag:guille.site,2017-09-19:/ls-images.htmlmathleast-squaresimage-processingPID as least squareshttps://guille.site/pid-ls.html<p>I want to say this is a folk theorem (borrowing terminology from game theory) in that everyone who does optimal control theory knows about this stuff, probably,<sup id="fnref-people"><a class="footnote-ref" href="#fn-people">1</a></sup> but I haven't really seen it stated explicitly anywhere. If anyone does indeed work on optimal control, I'd love to know your …</p>Guillermo AngerisWed, 13 Sep 2017 00:00:00 -0700tag:guille.site,2017-09-13:/pid-ls.htmlcontrol-theorymathleast-squaresThis blog is a liehttps://guille.site/blog-lie.html<p>(Maybe.)</p>Guillermo AngerisTue, 12 Sep 2017 00:00:00 -0700tag:guille.site,2017-09-12:/blog-lie.html