More on “Core Points”

A few additions to yesterday’s post occurred to me belatedly. First, it may be a good idea to check whether your alleged core point \(y^0\) is actually in the relative interior of the integer hull \(\mathrm{conv}(Y)\). A sufficient condition is that, when you substitute \(y^0\) into the constraints, all inequality constraints including variable bounds have …

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Finding a “Core Point”

In a famous (or at least relatively famous) paper [1], Magnanti and Wong suggest a method to accelerate the progress of Benders decomposition for certain mixed-integer programs by sharpening “optimality” cuts. Their approach requires the determination of what they call a core point. I’ll try to follow their notation as much as possible. Let \(Y\) …

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Gork revisited, 2018

It’s been almost 10 years since I made the post Are you Gork? Over the last decade, both scientists and non-scientists have become more confident that we will someday create: A. AGI (= sentient AI, named “Gork” :-)  See Rise of the Machines: Survey of AI Researchers. B. Quantum Computers. See Quantum Computing at a Tipping …

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Quantum Computing near a Tipping Point?

I received an email from a physicist colleague suggesting that we might be near a “tipping point” in quantum computation. I’ve sort of followed quantum computation and quantum information as an outsider for about 20 years now, but haven’t been paying close attention recently because it seems that practical general purpose quantum computers are still …

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Creating A New MIME Type

I struggled a bit this afternoon creating a new MIME type and associating it with a particular application, so I’m going to archive the solution here for future reference. This was on a Linux Mint system, but I found the key information in a GNOME documentation page, so I suspect it works for Ubuntu and …

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Thread Safety

As I noted in yesterday’s post, one of the major changes associated with the new “generic” callback structure in CPLEX is that users now bear the responsibility of making their callbacks thread-safe. As I also noted yesterday, this is pretty new stuff for me. So I’m going to try to share what I know about thread …

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CPLEX 12.8: Generic Callbacks

IBM is getting ready to release CPLEX 12.8, and I had the opportunity to attend a presentation about by Xavier Nodet at the 2017 INFORMS annual meeting. Here are links to two presentations by Xavier: CPLEX Optimization Studio 12.8 – What’s New and CPLEX 12.8 – the Generic Callback. As with any new release, there …

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Where are participants in American and Canadian teacher hashtags?

My dissertation research is focused on Regional Educational Twitter Hashtags (RETHs), which are teacher-focused hashtags that are associated with particular geographic regions, such as American states or Canadian provinces or territories. This isn’t the first time that I’ve done a project on this phenomenon, and it’s rewarding to come back to RETHs to answer some questions that …

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Minimizing a Median

\( \def\xorder#1{x_{\left(#1\right)}} \def\xset{\mathbb{X}} \def\xvec{\mathbf{x}} \)A somewhat odd (to me) question was asked on a forum recently. Assume that you have continuous variables \(x_{1},\dots,x_{N}\) that are subject to some constraints. For simplicity, I’ll just write \(\xvec=(x_{1},\dots,x_{N})\in\xset\). I’m going to assume that \(\xset\) is compact, and so in particular the \(x_{i}\) are bounded. The questioner wanted to …

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Rolling Horizons

I keep seeing questions posted by people looking for help as they struggle to optimize linear programs (or, worse, integer linear programs) with tens of millions of variables. In my conscious mind, I know that commercial optimizers such as CPLEX allow models that large (at least if you have enough memory) and can often solve …

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Robots taking our jobs

The figures below are from the recent paper Robots and Jobs: Evidence from US Labor Markets, by Acemoglu and Restrepo. VoxEU discussion: … Estimates suggest that an extra robot per 1000 workers reduces the employment to population ratio by 0.18-0.34 percentage points and wages by 0.25-0.5%. This effect is distinct from the impacts of imports, …

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Don’t Touch the Computer

Under what circumstances should humans override algorithms? From what I have read I doubt that a hybrid team of human + AlphGo would perform much better than AlphaGo itself. Perhaps worse, depending on the epistemic sophistication and self-awareness of the human. In hybrid chess it seems that the ELO score of the human partner is …

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Memory Minimization

As I grow older, I’m starting to forget things (such as all the math I ever learned) … but that’s not the reason for the title of this post. A somewhat interesting question popped up on Mathematics StackExchange. It combines a basic sequencing problem (ordering the processing of computational tasks) with a single resource constraint …

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Super-human Relational Reasoning (DeepMind)

These neural nets reached super-human (better than an average human) performance on tasks requiring relational reasoning. See the short video for examples. A simple neural network module for relational reasoning https://arxiv.org/abs/1706.01427 Adam Santoro, David Raposo, David G.T. Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, Timothy Lillicrap (Submitted on 5 Jun 2017) Relational reasoning is a …

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Face Recognition applied at scale in China

The Chinese government is not the only entity that has access to millions of faces + identifying information. So do Google, Facebook, Instagram, and anyone who has scraped information from similar social networks (e.g., US security services, hackers, etc.). In light of such ML capabilities it seems clear that anti-ship ballistic missiles can easily target …

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Premature Obituaries

[T]he report of my death was an exaggeration. (Mark Twain, 1897) In a recent blog post, “Data Science Is Not Dead“, Jean-Francois Puget discussed and dissented with a post by Jeroen ter Heerdt titled “Data Science is dead.” Barring the possibility that Schroedinger shoved data science into a box and sealed it, both assertions cannot …

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Rise of the Machines: Survey of AI Researchers

These predictions are from a recent survey of AI/ML researchers. See SSC and also here for more discussion of the results. When Will AI Exceed Human Performance? Evidence from AI Experts Katja Grace, John Salvatier, Allan Dafoe, Baobao Zhang, Owain Evans Advances in artificial intelligence (AI) will transform modern life by reshaping transportation, health, science, …

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Epistemic Caution and Climate Change

I have not, until recently, invested significant time in trying to understand climate modeling. These notes are primarily for my own use, however I welcome comments from readers who have studied this issue in more depth. I take a dim view of people who express strong opinions about complex phenomena without having understood the underlying …

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If This and That Then Whatever

I was asked a question that reduced to the following: if \(x\), \(y\) and \(z\) are all binary variables, how do we handle (in an integer programming model) the requirement “if \(x=1\) and \(y=1\) then \(z=1\)”? In the absence of any constraints on \(z\) when the antecedent is not true, this is very easy: add …

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Update Error: Wrong Architecture

Yesterday I ran into one of those mystifying glitches that, will infrequent, serve as a reminder that Linux is not for the faint of heart. When I booted my desktop system (Linux Mint 18.1 Serena), the system tray icon for the software updater was displaying a red “X” that indicates it tried and failed to …

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Yann LeCun on Unsupervised Learning

This is a recent Yann LeCun talk at CMU. Toward the end he discusses recent breakthroughs using GANs (Generative Adversarial Networks, see also Ian Goodfellow here and here). LeCun tells an anecdote about the discovery of backpropagation. The first implementation of the algorithm didn’t work, probably because of a bug in the program. But they convinced …

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Adventures with TeX Live

Since I use the Linux Mint operating system, the obvious (if not only) choice for a LaTeX distribution is TeX Live. (If you are not familiar with, or are not interested in, the LaTeX typesetting system, you have already read too far in this post.) On Mint, Ubuntu and other Debian-type operating systems, you typically …

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Another Absolute Value Question

Someone asked whether it is possible to eliminate the absolute value from the constraint \(Lx\le |y| \le Ux\) (where \(L\ge 0\) and \(U>0\) are constants, \(x\) is a binary variable, and \(y\) is a continuous variable). The answer is yes, but what it takes depends on whether \(L=0\) or \(L>0\). The easy case is when …

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Fischetti on Benders Decomposition

I just came across slides for a presentation that Matteo Fischetti (University of Padova) gave at the Lunteren Conference on the Mathematics of Operations Research a few days ago. Matteo is both expert at and dare I say an advocate of Benders decomposition. I use Benders decomposition (or variants of it) rather extensively in my …

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Pro Bono Analytics Is Growing Social

Pro Bono Analytics is a program by INFORMS (the Institute for Operations Research and the Management Sciences, for the acronym-averse), “the largest society in the world for professionals in the field of operations research (O.R.), management science, and analytics”. PBA “connects our members and other analytics professionals with nonprofit organizations working in underserved and developing communities”. …

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AlphaGo (BetaGo?) Returns

Rumors over the summer suggested that AlphaGo had some serious problems that needed to be fixed — i.e., whole lines of play that it pursued poorly, despite its thrashing of one of the world’s top players in a highly publicized match. But tuning a neural net is trickier than tuning, for example, an expert system …

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Mapping Trackball Buttons

For years, I’ve used a Logitech M570 wireless trackball with my Linux Mint PC. I generally prefer trackballs to mice — no need to lift and reposition after a bunch of movement — and I find that using my thumb, rather than my index finger (or, if I’m in a bad mood, my middle finger) …

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Mint Upgrade Woes

As I mentioned a couple of months ago, I upgraded a laptop from Linux Mint 17.3 (“Rebecca”) to 18.0 (“Sarah”) with minimal difficulties. My laptop serves as a guinea pig for these things. Once I’m sure things work fine on the laptop, I’ll consider upgrading my desktop as well. A few days ago I finally …

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