Longest Path Searchhttps://guille.site/Wed, 05 Jun 2019 00:00:00 -0700The S-procedure and small covering ellipsoidshttps://guille.site/covering-ellipsoid.html<p><em>Note:</em> This post was inspired by <a href="https://msl.stanford.edu/people/kunal-shah">Kunal Shah</a>'s question that came up at some point during one of our meetings: is there an efficient way of finding an ellipsoid which covers the intersections and unions of a bunch of other ellipsoids?</p>
<p>While this question has been explored <a href="https://pdfs.semanticscholar.org/ab38/565f7957f7ee4980663324b5820b0a018de2.pdf">somewhat</a> <a href="http://www.optimization-online.org/DB_FILE/2018/07/6719.pdf">extensively …</a></p>Guillermo AngerisWed, 05 Jun 2019 00:00:00 -0700tag:guille.site,2019-06-05:/covering-ellipsoid.htmlmathcontrol-theoryS-procedurePhysics, optimization, and impossibilityhttps://guille.site/physics-impossibility-results.html<p><em>Note:</em> this post is based on the results of <a href="https://arxiv.org/abs/1811.12936">this arXiv paper</a> which I've been working on with Stephen Boyd and Jelena Vuckovic.</p>
<p>The main result of the above paper is kind of weird: essentially, it turns out that you can say what devices are physically <em>impossible</em> by phrasing certain …</p>Guillermo AngerisMon, 17 Dec 2018 00:00:00 -0800tag:guille.site,2018-12-17:/physics-impossibility-results.htmloptimizationmathphysicsresearchMarkov processes and the second lawhttps://guille.site/second-law-markov.html<p><em>Note:</em> This is another one of those "quick" posts about a topic I've found to be fascinating, but which is almost never discussed.</p>
<p>Physics has this nice little law called the <a href="https://en.wikipedia.org/wiki/Second_law_of_thermodynamics">second law of thermodynamics</a>, which governs every physical thermodynamical system in question. The second law is usually phrased as …</p>Guillermo AngerisThu, 13 Sep 2018 00:00:00 -0700tag:guille.site,2018-09-13:/second-law-markov.htmlstatisticsmathinformation-theoryphysicsquick-postMachine learning, information, and tail boundshttps://guille.site/ml-information-bounds.html<p>Usually, in explaining the connection between information theory and machine learning, I would begin by writing down the definition of entropy and deriving some useful results about it, and then come back to tell you that you can look at ML as an information problem, where nature picks some parameters …</p>Guillermo AngerisTue, 04 Sep 2018 00:00:00 -0700tag:guille.site,2018-09-04:/ml-information-bounds.htmlstatisticsmathinformation-theoryPCA 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 once 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-theoryauvsiProximal 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