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Applied Mathematical Programming (1977)
- psykotic 10y ago'Programming' as in linear programming, dynamic programming, etc, not 'programming' as in computer programming.
- pabb 10y agoI won't assume that someone on HN wouldn't potentially benefit from this, but it honestly seems like OP submit this without reading the first sentence of the first page. That, or this was blatant trolling of some benign fashion.
- princeb 10y agomanagement science is a great topic and is one of the important applications of various optimization algorithms in mathematics. it's roughly the same field as industrial engineering. most people get by just figuring out how to put problems in excel and hit "SOLVER" (or Matlab and fmincon) but there is some value in figuring out the algorithm works. then it's a hop skip and jump away from the other classes of optimization that you see in machine learning.
- graycat 10y agoIn practice, the real problems don't have to get very large or complicated before just typing the problem into AMPL or clicking on SOLVE won't work -- that is, solver capacities may be exceeded or the running time can become absurdly long. Then you must exploit whatever special structure you can find in your problem and dig into the algorithms to make refined usage. So, maybe do some Lagrangian relaxation. Maybe find an embedded network flow problem and use a network flow version of the simplex algorithm.
- vitaut 10y agoMathematical programming (optimization) has so many useful applications and I am very pleased to see this classical book on the topic available online. Unfortunately because it has been written a while ago it doesn't cover algebraic modeling languages and examples are in Excel which is not an adequate optimization or teaching tool (even XKCD has something to say about it in his webcomic https://xkcd.com/1667/ https://xkcd.com/1667/).
- kxyvr 10y agoI'm glad there's more free material online for optimization modeling and algorithms. Personally, here's my favorite list for algorithms and modeling for optimization: For learning the simplex method, Linear Programming by Vasek Chvatal (first 10 chapters): https://books.google.com/books?id=DN20_tW_BV0C&printsec=frontcover https://books.google.com/books?id=DN20_tW_BV0C&printsec=fron... For learning branch and bound, Integer Programming by Laurence A. Wolsey https://books.google.com/books?id=x7RvQgAACAAJ https://books.google.com/books?id=x7RvQgAACAAJ For odd modeling tricks for integer programming, Logic and Integer Programming by Williams, H. Paul https://www.springer.com/us/book/9780387922799 https://www.springer.com/us/book/9780387922799 For modeling tricks for convex programming, Convex Optimization by Stephen Boyd and Lieven Vandenberghe https://stanford.edu/~boyd/cvxbook/ https://stanford.edu/~boyd/cvxbook/ For basic nonlinear optimization algorithms, Numerical Optimization by Nocedal, Jorge, Wright, S. https://www.springer.com/us/book/9780387303031 https://www.springer.com/us/book/9780387303031 I've never really found the ultimate optimization book, but the references above tend to have the right modeling techniques, algorithms, and references. I've found they're a good place to get the right idea and the right words to search for more material.
- vitaut 10y agoJust to add, the book "AMPL: A Modeling Language for Mathematical Programming" by Robert Fourer, David M. Gay, and Brian W. Kernighan (yes, the "K" in K&R) is also freely available online: http://ampl.com/resources/the-ampl-book/chapter-downloads/ http://ampl.com/resources/the-ampl-book/chapter-downloads/ . It is not only a reference for the AMPL modeling language, but also a great introduction to mathematical optimization.
- codepie 10y agoYou can add the optimization course on coursera https://www.coursera.org/course/optimization https://www.coursera.org/course/optimization to your list. I have been waiting for it to start and it seems that it is finally going to start this month (https://class.coursera.org/optimization-003/forum/thread?thread_id=266 https://class.coursera.org/optimization-003/forum/thread?thr...).
- cschmidt 10y ago
- eggy 10y agoOld, but after skimming it for an hour, it seems very applicable. I had been researching genetic algorithms to do scheduling optimization in the past based on a 1996 thesis 'A Genetic Algorithm for Resource-Constrained Scheduling' [1] (PDF download alert). I am not an operations manager, but I seem to always have a need to perform similar analyses or be in a position to comment on others. Operations management texts tend to be very broad, or geared to a non-mathematical manager, so I am finding more texts like this one to be more enjoyable and informative for my purposes. The last optimization problem WRT to OM I worked on was to review an OEM's recommended spares list for validity given lead times on certain items, and the FMEA (Failure Modes and Effects Analysis) to see how many of each spare, and when we should order replenishments to achieve a 95% or greater confidence level that we would have stock of a particular item, and not have any downtime. There is huge software that automatically does this for large companies, but for little to mid-level companies, it is great to be able to dig in to the algorithms to gain a better understanding, and heck, just for the fun and learning experience especially when said company doesn't see the benefit of the larger software. Thanks for the link! [1] http://lancet.mit.edu/~mbwall/phd/thesis/thesis.pdf http://lancet.mit.edu/~mbwall/phd/thesis/thesis.pdf
- graycat 10y agoThis book is comparatively old, but the authors are experts, and likely the material is still surprisingly current. But I will insert another point, call it the "Dirty Little Secrets of Optimization Your Books and Professors Don't Tell You." Here is a bottom line, bold, summary fact of life about such optimization, mathematical programming, operations research: It's super tough to find real world problems where can apply such material, do well on the problems, please the customers, and get paid well enough to have a career. Trying such work either as a consultant or an employee is tough. There are exceptions, but they are rare. If you can find an exception, terrific, but, did I mention, they are rare. Nearly anything else you can do with a BS, MS, or Ph.D. in a STEM field will be an easier way to make a living. In practice, the field has a bad reputation: Early on there was a lot of hype and a lot of projects that failed. Leading reasons for project failure were (1) the basic data was too difficult to collect, (2) some custom software was needed, and it was too difficult to write, (3) the available optimization software was not powerful enough, (4) the mathematical techniques were not powerful enough, at least not without a lot of special work unique to the particular practical problem, (5) the computer run times were too long, too often days or weeks. In addition there were various social problems: So, the optimization people were seen as wizards with tall, conical black hats decorated with stars and moons and were not really welcome, were not understood, were threatening, etc. Here is a larger problem: The optimization people did not have a recognized profession. Lawyers, physicians, insurance actuaries, and more do have a recognized profession, maybe with government licensing, a code of ethics, professional peer review, legal liability, graduate education which is not just academic but also professional, likely with practical apprenticeship, a serious professional society, professional certification, etc. That way, a generalist line manager can hire a respected professional, as an employee or consultant, with relatively low risk to his career. Without professional status, such a line manager is reluctant and for good reason. Then there's another secret: Early on, when there was a lot of optimism, there were two ideas, maybe just implicit but, still, powerful: The first idea was that such optimization would, to borrow a more recent phrase, "eat the world". That is, essentially every economic activity in the world would be directed by such optimization. The second idea was that the optimal solution was the absolute goal. Accepting a solution that was 10 cents away from optimal was seen as a moral lapse. The word optimal was a stick used to beat up on everything and everyone else. Then reality set in: The applied math available was nowhere nearly powerful enough to solve just any practical problems that could be found in routine operations. And that was just the clouds before the hurricane: The hurricane happened when the question P versus NP was formulated and, then, it was seen that large, practical problems in NP-complete were as common as pebbles in a stream bed. Darned near every problem in scheduling, routing, logistics, resource allocation, and more could want at least something as difficult as integer linear programming, but that problem is in NP-complete. Then considering non-linear aspects gave a storm that made a hurricane look like a gentle rain. Then it got worse: A lot of real problems had a lot of randomness. Okay, a lot of those problems can be formulated as stochastic optimal control problems, maybe continuous time, maybe discrete time, but then get bad news right away: First don't have enough data on either the system dynamics or the probability distributions of the random effects. Second on realistic problems, stochastic optimal control can eat super computer time by the months per problem. The worst of the chuckholes in the road was the struggle of P versus NP. And with the moral attitude that optimal was to be obtained made the P versus NP challenge much worse. Indeed the US economy went for decades declining to implement solutions that could save 15% of operating costs because saving 16% for an optimal solution was too difficult for the math and the computing. That is, commonly saving that last 10 cents is by far the hardest. Or there might be millions of dollars to be saved, but still could not save the last 10 cents, and people gave up due to the difficulty of that last 10 cents. And there was a huge cultural problem: Various universities set up professorships, sometimes departments, concentrating on optimization. Well, there the professors concentrated on publishing papers and largely ignored real problems. And anything like professional education was pushed out as inferior to the research agenda. Then, sure, the students got relatively little benefit in non-academic careers -- e.g., they were not in a profession. For a while, there was an eager customer who did put up with a lot of the hype and poor or failed projects -- the US DoD. So, bottom line: A lot of very good applied math has been done for optimization. And there is a lot of high quality software. But real problems that can be attacked successfully with these tools and where the benefits are really worth the botheration, time, money, and effort are rare. If you can find suitable real problems and make a living, you will be very rare, but good for you. What will likely happen is that occasionally some optimization will become part of some software that is sold as, say, SaaS. And, in some fields where optimization is known to be effective, say, feed mixing, we can expect that optimization is an accepted tool in that field. So, what was the biggest result of the academic research? Sure, they identified the problem of P versus NP. Gads, I should have started a pizza shop!
- pasbesoin 10y agoThe link to the Excel Excercises is currently 403, but they are on archive.org: http://wayback.archive.org/web/20150309105904/http://web.mit.edu/15.053/www/ExcelExercises/ http://wayback.archive.org/web/20150309105904/http://web.mit...
- ejanus 10y agoAny easy-to-understand materials?