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George Dantzig, 1914-2005
Markus Registrada writes "George Dantzig, the inventor of the Simplex method for solving Linear Programming problems, died on May 13. He was also the now-legendary student who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems."
Goodbye, dear friend.
We hardly knew ye.
And we certainly had no idea what you were talking about.
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At least his teachers knew he wasn't cheating.
R.I.P., Dude.
"Linear programming" (as well as "mathematical programming", "convex programming", etc.) has little to do with computer programming. It's about finding the solution to problems like maximize f(x) subject to restrictions r1(x)=0 .. rn(x)=0, r1(x)>0... rn(x)>0.
Incidentally, the Simplex method -- unlike differential calculus-based methods for more general problems like the Kuhn-Tucker method -- is quite programmable on a computer, and quite efficient.
Here's a FAQ: http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-p rogramming-faq.html
What is most interesting about LP is not that it is just a method of finding the solution to a problem, but that it extends in range over many diverse fields from (obviously) computer programming to fields such as economics and even business planning.
It's always sad when a great scientific mind dies. And I recall, just recently, someone was joking about using the simplex method to find the best seat in a theater to see Star Wars.
Cyde Weys Musings - Scrutinizing the inscrutable
If so, George has certainly earned a look at The Book. (The one containing all possible mathematical theorems...)
Paleotechnologist and connoisseur of pretty shiny things.
"He was also the now-legendary student who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems."
How to get a date?
Now this is why I read Slashdot - where else can you get such a diverse range of people, and pick up wonderful little tidbits like the true story behind that wonderful legend about solving unsolved problems? Sure, it's available on Snopes for you to find if you know what you're looking for, but asking the right question is often a lot harder than the answer, as best illustrated bythe Hitch Hiker's guide: Meaning of life=42, Question=???. (Hey, perhaps if they'd put that up on the board, he might have been able to solve that as well!)
Physicist, consultant, science communicator
"examples of what were suspected to be unsolvable problems" No big deal, I do unsolvable homework problems all the time.
If he was so smart, why did he make the mistake of thinking it was homework?
Since neither link indicated that Mr. Dantzig had actually died, here is a link to the San Jose Mercury News article on him.
Quadratic Programming is used in solving portfolio optimisation problems, a mathematical way to ensure a portfolio of risky assets are diversified.
:P
Well, to backtrack a bit, we can use linear programming for making predictions "pragmatically". Think the lame old spreadsheet neural net
I mean, saying that linear programming has little to do with computing kind of slaps the best program ever made in its face.
The Spread Sheet (I default to Excel, but insert you fav modern flavor)
Excel is probably the most powerful, robust, versatile, used for everything and the kitchen sink, program ever created. It's a freaking Swiss army knife, and it's because of Linear Programming.
We may not directly use it (ever), but Linear Programming has shaped modern computing as we know it.
There are way too many applications to list here. Ill give you an example though. Say you are a company that produces Chairs and Tables. You sell chairs for $10 and tables for $20. It costs you 5 units of wood to make a chair and 8 units of wood to make a table. It costs you 2 units of labour to make a chair and 3 units of labour to make a table.
Now say you have a certain amount of wood and labour to "spend", how much of each product should you produce to max yield, min waste, min cost, max profit...All different objectives give different answers.
This is a simple example that can be solved without simplex but if you were to scale it up to 1000 products with 3000 resources to be split, it can still be solved with the simplex algorithm.
I have written my own simplex solver and they are tricky but the basic algorithm is elegant.
Of course, the example I gave above is only one and there are many applications in the area of Operations Research (thats not my field btw).
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What happend to me was the opposite.
A few years ago my math teacher gave us an exam with one particular problem that I couldn't solve. (Apparently a typo or misplaced sign made a rather simple problem into an unsolvable one).
So I went to the library, researched on the problem, and found out it was unsolvable. I PROVED IT mathematically, but the teacher didn't believe me.
And my grade wasn't changed! Doesn't that suck!?
Lesson to be learned: Life's not fair. SPECIALLY with underpaid teachers designing the exams. Hmph.
It's times like these we need a moderation option of "-1, crack baby".
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Linear programming was among the first "real" applications of digital computers. I saw Dantzig give a talk about it at an INFORMS conference back in the 1980s.
t ml.) It seems that Von Neumann understood everything pretty much immediately, and even derived the dual solution to LP in the first sitting.
...
It seems that in a visit to Von Neumann in 1947 he described LP and the simplex method a bit. (See http://www.pupress.princeton.edu/chapters/i7802.h
I suppose we all know what Von Neumann did next
I can't help but think if he ever would have solved those problems had he been taught first that they were unsolvable??
Schizo Person #1- "Look, there is an elephant in the room"
Schizo Person #2- "Shhh!!! There is no elephant"
Schizo Person #1- "But..."
Schizo Person #2- "No buts, you don't want them to think you're crazy"
Soon Schizo Person #1 stopps seeing the elephant. It really does not exists to him
Rosco: "If brains were gunpowder, Enos couldn't blow his nose."
Translation for today's college students. :-)
Link
I wish my lawn was emo, so it would cut itself.
Am I the onlyone who read this and initially thought something along the lines of "what does Glenn Danzig have to do with Pi"?
hehe, I was thinking about applying the LP solving technique to these types of games but they made it difficult...For example, in warcraft 3, there are different types of armour and "attacks". So you have to choose which type of armoured and attack units to make. I am very certain that Blizzard looked at the linear space and made sure that the constraints in the system all had the same n-dimensional slope.
:)
A few years ago, I looked into it for night elves and that was the case for a few units.
Either way, if the game did have some inbalance, you *could* find it if you could be bothered
Can your karma go above being Excellent?
Well folks, I'm an accountant. You can have all the fun you want about having an accountant here, but that's the way it is. In Argentina, where I come from, that was the best way to land a management position in no time, which I'm still waiting for.
/.
All that aside, I love technology in all its forms, just in case.
Studying my 4th year, we've been teached LP, as a way to solve transport route problems, and minimum stock estimates, optimizing resources and stuff, in an assignment called "Operations Research".
I hope one of my fellow students will read this, but I really doubt an graduate from Facultad de Ciencias Economicas - Universidad Nacional de Cordoba would read
We always dreamed about finding the damn mf that invented the simplex method, but the net was far from being an accesible thing those days, so now that I find out about Dantzig, I'm kinda sad. There was a time when I would have cursed his family and chased him if he was within reach, but now I pay him honors, as one of many bright minds that go by unnoticed for students and developing minds all over the world.
My respect
I just read
I'm sad to say Leonid Khachiyan also died recently. He proved that linear programming can be solved in polynomial time with the ellipsoid method. I took a class on algorithms from him many years ago at Rutgers. He was an excellent teacher, and he will be missed.
Chris Mesterharm
...if you had a unique goal function and linear equations perhaps. First of all, you are playing against an opponent, so the optimal strategy will depend on his strategy. If they have done this well, there should be a "scissors-paper-rock" balance with no dominant strategy. Secondly, the strength of a battle group is not linear (that is why you have a certain mix of heavy fortifications, long-range artillery, light troopers etc etc). It's not like you can describe it as A*x1+B*x2+C*x3.... = strength, because any one troop type alone would probably be wiped out quickly (unless you have a dominant type, which would make the game rather silly).
Kjella
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