It has only week on Linear Programming which is nicely done but I think the real value is that it starts with the much more playful Constraint programming and focuses on intuitions and keeping you both entertained and trained which is really hard to do.
The course comes with assignments and the whole thing sort of has a Advent of Code flavor (I kind of have a half baked plan on make this year discrete optimization my AOC theme).
Not strong on the modeling part/business motivation.
On the Optimization Ph.D. qualifying exam, got a "High Pass" and the best score in the class.
In optimization answered a question in the Kuhn-Tucker constraint qualifications and had the paper accepted quickly in Mathematical Programming.
Taught linear programming in a well-known business school for 5 years.
NYC had a few users, in a loose group, of linear programming but were not very good at it. Somehow I stumbled into the group and was by far the best, but there was no chance of a career or job there.
Net, saw next to nothing in "applied". Believing "applied" would have been homeless living on the street, exactly, no exaggeration.
Was not able to help my wife -- she died. Had two cats. They got sick, needed medical care I couldn't afford, and died.
Thousands of resume copies posted -- no meaningful responses.
The Sheriff showed up with several workers with guns, dumped all my clothes, furniture, music materials, e.g., piano, large professional library on the front -- I had to drive off with a few items.
At FedEx I saw a good application, got a memo from the Founder, COB, CEO to pursue it, pleased two crucial members of the BOD, saved FedEx twice, but one manager tried to fire me,
another said there was "no money in the budget" for me, the stock promised in 3 weeks was WAY late, and I'd been commuting between Memphis and Maryland.
Could have done better with a lawn mowing company, LITERALLY.
Actually, big picture: Heavily long, likely still, the main US customer, apparently 99+%, for optimization of any kind was US national
security.
I was manipulated, fooled, and very seriously hurt by the claim "applied".
A fact of life: Nearly always people with money, power, and optimization problems don't understand optimization, fear and resent those who do, and choose just to avoid the subject.
So, no wife, no cats, starting a business, no boss, sole-solo founder, do have some original applied math deep in the technology, and face just US Internet startup reality.
Optimization? Get a 2 hour overview and otherwise f'get about it.
The point of the post is that in my long experience there was not much about optimization that in any significant practical career sense was "applied", i.e., no jobs even to keep one from living on the streets, far from a career to buy a house and support a family.
The point about my Ph.D. with a lot in optimization is that I was quite well qualified in the field, but even with all those qualifications "applied" was not real, i.e., there just was nothing like a career in optimization applications.
Can suspect that, yes, "Ph.D." did seriously damage all career prospects, optimization, math, even computing.
The successes I did have were in computing. At the time the math was a small aid.
Did get paid for some work in applied optimization on some military problems. Looking back, there was some stranger in the office eager to discuss the weather, etc. with me. Maybe I said the wrong things about some of the US foreign wars, and then the stranger was gone. Might have been some high end military job interview that needed only gung ho attitudes toward foreign policy.
Delicate political situation, and I was oblivious about politics. Like, "stick to two subjects, the weather and everyone's health" and avoid "sex, politics, and religion".
Early on while I was in a grad program teaching math, some recruiters came from DC desperate for anyone with some math/physics education. I interviewed: Got a offer and took a job right away. Soon bought a new car and got married.
In those days, around DC, to get a job, just look in the WaPo, apply, go on the interview, show some knowledge of some of computing, get an offer, compare a few offers, with, say, a 15% raise, and accept one -- worked great. For a while, at GE time sharing national HQ, was the main guy for the applied math library, e.g., the FFT, regression analysis. Later a good background in "applied" optimization, worthless.
> A fact of life: Nearly always people with money, power, and optimization problems don't understand optimization, fear and resent those who do, and choose just to avoid the subject.
Food for thought: the solution to real-world optimization problems is often dictated by constraints instead of optimal values.
This means that if you fail to understand the constraints, or even fail to identify them, then whatever your solution to the problem is, it will be wrong. And it will be obvious to those who are aware of the constraints.
Now, you're complaining that those presenting you with problems "don't understand optimization".
From your anecdotes you were the one tasked with clarifying things to them. From the sound of it, you didn't accomplished that, and it was unclear to stakeholders whether your output even provided any value worth keeping.
Have you ever considered the possibility that you failed to understand the actual problems presented to you and even failed to clarify why your output was aligned with anyone's best interests?
Naw, you list some mistakes, but I didn't make any of those.
> From your anecdotes you were the one tasked with clarifying things to them. From the sound of it, you didn't accomplished that, and it was unclear to stakeholders whether your output even provided any value worth keeping.
First, for any application, there has to be some practical interest. My view, there isn't much. The schools of math, engineering, and business have given optimization a big push, back at least to Dantzig, but from my long experience the interest was and is still just too low for "applied" optimization to have much in applications.
Cases: Sure, there has been a professor at Princeton who applied optimization to oil refining: What mixture of crude oil to mix into the refinery and what mixture of refined products to take out. Maybe a few, large livestock operations actually do run some diet problem solutions. And can use 0-1 optimization for Sudoku problems? What path for picking orders in a big warehouse, for Amazon or Walmart? A simple traveling salesman problem, and for a good enough solution build a minimum spanning tree and walk around that -- maybe they are doing that already. Assembly line balancing: Assign workers to positions to maximize the speed of the slowest worker assignment. Is anyone actually doing that? Even if they are, the solution is quite simple. Yes, a start on P vs NP was at Bell Labs designing networks. So, maybe with the Internet there are still valuable applications? Considered that. Got an interview at a company trying that. They were impressed by what I'd done at FedEx, but they were nearly dead and, I suspect, soon died. Maybe with big logistics, ocean, rail, trucks, warehouses, there are some big logistics problems where optimization could save a lot -- applications enough for careers? Better than grass mowing? When I got my Ph.D., the Chair of my dissertation orals committee was a big name in logistics -- saw no evidence
of significant interest in applications. No ones in the halls. Phone not ringing. No suggestions of contacts for me.
Look, when there is a big need, ESPECIALLY when there is big money involved, it soon gets obvious, and the US economy gets to it right away. In that, "applied" optimization is not hot, warm, or much above freezing.
Right, you are mentioning formulation:
(1) They had already formulated a 0-1 optimization problem. It had 40,000 constraints and 600,000 variables. They had tried the then popular simulated annealing, ran for days, and quit. So, the formulation was done and not mine.
I worked hard, with the IBM OSL (optimization subroutine library), did 900 primal-dual iterations, Lagrangian relaxation, got a feasible solution within 0.025% of optimality, within two weeks, for free, a free sample, and never heard from them again. They resented and were afraid of my success.
(2) Another company was working a little more generally in optimization. Had a crude heuristic running. On some of their problems, 0-1, linear, again was successful with the OSL, and got only insults and resentment. Continued on, gave them a nice formulation, better than their heuristic, and path through optimization, and got fired. They'd hired me and wanted to fire me before 6 months was up. They were not very good with linear programming at all, and I was a LOT better at what they were doing in the formulation, math, and computing, and their reaction was they didn't want me for competition.
(3) In a military group, did well with some non-linear optimization (their formulation). Then they had a challenging strategic problem. I did a formulation of a Monte-Carlo solution and wrote and ran the code (used an Oak Ridge random number generator I'd programmed in assembler). They called in a famous probability professor for a review. His remark was that there was no way the Monte-Carlo could "fathom" the tree. He was right; the tree was huge. But each trial of my Monte-Carlo yielded at each point in time a random variable on 0-15, and the law of large numbers applied right away. It wasn't D-day, but suppose it was: The tree of possibilities was enormous, but the, say, number of Allied soldiers killed was, what, 0-200,000. So, each trial give a random variable value at, say, each second, for, say, 48 hours -- the law of large numbers applies and could tell Ike the distribution of number of deaths, the expected values, the median, the variance for each second of the 48 hours. Passed the review. One guy there used my random number generator on one of his old problems, got significantly different results, was afraid, said "I don't want you in the center of all my projects", and I got ignored on the way to being fired.
(4) At FedEx, had written a program that showed the BOD that the program made the fleet scheduling easy enough and saved the company. So, to do better, formulated a set covering direction. Savings? 1% would have been $millions a year. The founder, COB, CEO wrote a memo making that my project, but my boss, a Senior VP, said that there was no money in the budget for me; I'd been commuting between Memphis and Maryland where my wife was in her Ph.D. program; the stock promised in three weeks was very late; and I went for a Ph.D.
Actually another student at another school ran with my set covering formulation for his dissertation.
The high level, overview, simple fact of life, is as I described: There just is no real career in "applied" optimization. That horse is nearly dead and should not be further flogged. Millions of US families have a house, stable marriage, and healthy children, and I'd believe that fewer than 20 of those families are supported by careers in "applied" optimization -- maybe 0 families.
> A fact of life: Nearly always people with money, power, and optimization problems don't understand optimization, fear and resent those who do, and choose just to avoid the subject.
Worth considering this hard question: who optimized their life better? Them or us?
Yup. Applied Optimization 101: For decisions in life and career, avoid the applied math approach to optimization.
In particular, except maybe for some work in US national security, don't try to have the applied math of applied optimization for a career. Don't spend a lot of time studying optimization.
Later might be able to be the founder, COB, CEO of a startup where some math is a big advantage.
Hey I'm just replying because I currently have a BSc with Honors in math and a double major with econ but I'm having trouble in the current market. I also am interested in pursuing a master's in combinatorics or optimization. Is there anything you recommend besides not getting the PhD?
Bro, you spend a really long time getting great at this and from the bottom of my heart I feel your pain and believe we need to improve a lot as a society to take advantage of talents like you better.
Thanks for investing so much time to it, I share your sadness for your wife and hope you get ao much good as you tried to bring to the world, man
Just yesterday I sketch a solver for a board game: "Search for planet X".
The objective of the game is to figure out what kind of planets are hidden in sector of the boards using clues like: "There are 2 comets between secotr 3 and 7" or "No comet is next to an asteroid ".
Sketching the solver was incredibly fun and rewarding!
This was posted as a comment on a thread about a new Google tool for LP [0]. It was in response to someone asking for resources on learning linear programming for business applications. It looks like the examples have been solved using Excel, and it's for business students at MIT. Definitely not cutting edge.
The original posting is about new tools and algorithms, with some more analysis. Well beyond my background from undergrad courses in LP and OR, but probably more relevant and insightful to you.
The tools probably have changed but the fundamental language is the same. The same way that you need to wire your brain to see how a problem can be casted as a dynamic programming one, you also need to learn how to formulate problems as integer/linear programming ones.
For example all of the "hard" leetcode problems can be casted as math programming ones. But the interviewers will not appreciate this solution approach lol.
Once you conquer the logic/language then learning the tools is the easy part.
> But the interviewers will not appreciate this solution approach lol.
I once witnessed a programmer with a PhD in Maths find closed form formulas for a lot of questions where it was expected to write some code with loops building/accumulating a result. As a simple example, to explain what was going on, if the question would be "calculate the 100th fibonacci number", she would just use Binet's formula to do so (as opposed to using a loop). I was rather impressed how often that happened.
Depending on the job, interviewer gripes may be legitimate, or at least they should give you the opportunity to write a different type of solution.
If they’re writing a compartmentalized library specific to their domain, it’s fine. I’ve worked with a Stats PhD doing that.
If you’re dropping them into a shared codebase, the comprehensibility of their code to the other people on their team is essential. Great code that depends on knowledge no one else on the team has is not great. You end up with “That’s going to take forever to change, Steve wrote it”.
Agree, I‘d say also the term „mathematical programming“ sounds really old school and never was that fitting to begin with.
„Learning how to formulate problems as integer/linear programming ones“, as another commenter put it, works great if it‘s a natural fit and sure is fun for idk 7th grade math text problems I guess but OTOH squeezing realistic problems into systems of hundreds of equations (or more if dealing with linearizations of inherently non-linear/concave/multi-step problems) to satisfy tool idiosyncracies calls for additional tools in your arsenal.
Based on the code output in the book, it is old. But the book seems pretty easy to follow even if you are not strong in math. Hopefully, in the near future I will be able to pass a book like this to an LLM and have it enrich it with code examples in a programming language I am familiar with.
Readit News
However, I've found a cheat sheet to be much more helpful and practical for MIPs (not LPs but MIPs):
https://msi-jp.com/xpress/learning/square/10-mipformref.pdf
This contains the primitives you typically use in MIPs.
Deleted Comment
It has only week on Linear Programming which is nicely done but I think the real value is that it starts with the much more playful Constraint programming and focuses on intuitions and keeping you both entertained and trained which is really hard to do.
The course comes with assignments and the whole thing sort of has a Advent of Code flavor (I kind of have a half baked plan on make this year discrete optimization my AOC theme).
Not strong on the modeling part/business motivation.
On the Optimization Ph.D. qualifying exam, got a "High Pass" and the best score in the class.
In optimization answered a question in the Kuhn-Tucker constraint qualifications and had the paper accepted quickly in Mathematical Programming.
Taught linear programming in a well-known business school for 5 years.
NYC had a few users, in a loose group, of linear programming but were not very good at it. Somehow I stumbled into the group and was by far the best, but there was no chance of a career or job there.
Net, saw next to nothing in "applied". Believing "applied" would have been homeless living on the street, exactly, no exaggeration.
Was not able to help my wife -- she died. Had two cats. They got sick, needed medical care I couldn't afford, and died.
Thousands of resume copies posted -- no meaningful responses.
The Sheriff showed up with several workers with guns, dumped all my clothes, furniture, music materials, e.g., piano, large professional library on the front -- I had to drive off with a few items.
At FedEx I saw a good application, got a memo from the Founder, COB, CEO to pursue it, pleased two crucial members of the BOD, saved FedEx twice, but one manager tried to fire me, another said there was "no money in the budget" for me, the stock promised in 3 weeks was WAY late, and I'd been commuting between Memphis and Maryland.
Could have done better with a lawn mowing company, LITERALLY.
Actually, big picture: Heavily long, likely still, the main US customer, apparently 99+%, for optimization of any kind was US national security.
I was manipulated, fooled, and very seriously hurt by the claim "applied".
A fact of life: Nearly always people with money, power, and optimization problems don't understand optimization, fear and resent those who do, and choose just to avoid the subject.
So, no wife, no cats, starting a business, no boss, sole-solo founder, do have some original applied math deep in the technology, and face just US Internet startup reality.
Optimization? Get a 2 hour overview and otherwise f'get about it.
I am sensitive to your hardship, but optimization has nothing to do with it. People are succeeding with bachelor’s degrees in Latin.
The point about my Ph.D. with a lot in optimization is that I was quite well qualified in the field, but even with all those qualifications "applied" was not real, i.e., there just was nothing like a career in optimization applications.
Can suspect that, yes, "Ph.D." did seriously damage all career prospects, optimization, math, even computing.
The successes I did have were in computing. At the time the math was a small aid.
Did get paid for some work in applied optimization on some military problems. Looking back, there was some stranger in the office eager to discuss the weather, etc. with me. Maybe I said the wrong things about some of the US foreign wars, and then the stranger was gone. Might have been some high end military job interview that needed only gung ho attitudes toward foreign policy.
Delicate political situation, and I was oblivious about politics. Like, "stick to two subjects, the weather and everyone's health" and avoid "sex, politics, and religion".
Early on while I was in a grad program teaching math, some recruiters came from DC desperate for anyone with some math/physics education. I interviewed: Got a offer and took a job right away. Soon bought a new car and got married.
In those days, around DC, to get a job, just look in the WaPo, apply, go on the interview, show some knowledge of some of computing, get an offer, compare a few offers, with, say, a 15% raise, and accept one -- worked great. For a while, at GE time sharing national HQ, was the main guy for the applied math library, e.g., the FFT, regression analysis. Later a good background in "applied" optimization, worthless.
Food for thought: the solution to real-world optimization problems is often dictated by constraints instead of optimal values.
This means that if you fail to understand the constraints, or even fail to identify them, then whatever your solution to the problem is, it will be wrong. And it will be obvious to those who are aware of the constraints.
Now, you're complaining that those presenting you with problems "don't understand optimization". From your anecdotes you were the one tasked with clarifying things to them. From the sound of it, you didn't accomplished that, and it was unclear to stakeholders whether your output even provided any value worth keeping.
Have you ever considered the possibility that you failed to understand the actual problems presented to you and even failed to clarify why your output was aligned with anyone's best interests?
> From your anecdotes you were the one tasked with clarifying things to them. From the sound of it, you didn't accomplished that, and it was unclear to stakeholders whether your output even provided any value worth keeping.
First, for any application, there has to be some practical interest. My view, there isn't much. The schools of math, engineering, and business have given optimization a big push, back at least to Dantzig, but from my long experience the interest was and is still just too low for "applied" optimization to have much in applications.
Cases: Sure, there has been a professor at Princeton who applied optimization to oil refining: What mixture of crude oil to mix into the refinery and what mixture of refined products to take out. Maybe a few, large livestock operations actually do run some diet problem solutions. And can use 0-1 optimization for Sudoku problems? What path for picking orders in a big warehouse, for Amazon or Walmart? A simple traveling salesman problem, and for a good enough solution build a minimum spanning tree and walk around that -- maybe they are doing that already. Assembly line balancing: Assign workers to positions to maximize the speed of the slowest worker assignment. Is anyone actually doing that? Even if they are, the solution is quite simple. Yes, a start on P vs NP was at Bell Labs designing networks. So, maybe with the Internet there are still valuable applications? Considered that. Got an interview at a company trying that. They were impressed by what I'd done at FedEx, but they were nearly dead and, I suspect, soon died. Maybe with big logistics, ocean, rail, trucks, warehouses, there are some big logistics problems where optimization could save a lot -- applications enough for careers? Better than grass mowing? When I got my Ph.D., the Chair of my dissertation orals committee was a big name in logistics -- saw no evidence of significant interest in applications. No ones in the halls. Phone not ringing. No suggestions of contacts for me.
Look, when there is a big need, ESPECIALLY when there is big money involved, it soon gets obvious, and the US economy gets to it right away. In that, "applied" optimization is not hot, warm, or much above freezing.
Right, you are mentioning formulation:
(1) They had already formulated a 0-1 optimization problem. It had 40,000 constraints and 600,000 variables. They had tried the then popular simulated annealing, ran for days, and quit. So, the formulation was done and not mine.
I worked hard, with the IBM OSL (optimization subroutine library), did 900 primal-dual iterations, Lagrangian relaxation, got a feasible solution within 0.025% of optimality, within two weeks, for free, a free sample, and never heard from them again. They resented and were afraid of my success.
(2) Another company was working a little more generally in optimization. Had a crude heuristic running. On some of their problems, 0-1, linear, again was successful with the OSL, and got only insults and resentment. Continued on, gave them a nice formulation, better than their heuristic, and path through optimization, and got fired. They'd hired me and wanted to fire me before 6 months was up. They were not very good with linear programming at all, and I was a LOT better at what they were doing in the formulation, math, and computing, and their reaction was they didn't want me for competition.
(3) In a military group, did well with some non-linear optimization (their formulation). Then they had a challenging strategic problem. I did a formulation of a Monte-Carlo solution and wrote and ran the code (used an Oak Ridge random number generator I'd programmed in assembler). They called in a famous probability professor for a review. His remark was that there was no way the Monte-Carlo could "fathom" the tree. He was right; the tree was huge. But each trial of my Monte-Carlo yielded at each point in time a random variable on 0-15, and the law of large numbers applied right away. It wasn't D-day, but suppose it was: The tree of possibilities was enormous, but the, say, number of Allied soldiers killed was, what, 0-200,000. So, each trial give a random variable value at, say, each second, for, say, 48 hours -- the law of large numbers applies and could tell Ike the distribution of number of deaths, the expected values, the median, the variance for each second of the 48 hours. Passed the review. One guy there used my random number generator on one of his old problems, got significantly different results, was afraid, said "I don't want you in the center of all my projects", and I got ignored on the way to being fired.
(4) At FedEx, had written a program that showed the BOD that the program made the fleet scheduling easy enough and saved the company. So, to do better, formulated a set covering direction. Savings? 1% would have been $millions a year. The founder, COB, CEO wrote a memo making that my project, but my boss, a Senior VP, said that there was no money in the budget for me; I'd been commuting between Memphis and Maryland where my wife was in her Ph.D. program; the stock promised in three weeks was very late; and I went for a Ph.D.
Actually another student at another school ran with my set covering formulation for his dissertation.
The high level, overview, simple fact of life, is as I described: There just is no real career in "applied" optimization. That horse is nearly dead and should not be further flogged. Millions of US families have a house, stable marriage, and healthy children, and I'd believe that fewer than 20 of those families are supported by careers in "applied" optimization -- maybe 0 families.
Worth considering this hard question: who optimized their life better? Them or us?
In particular, except maybe for some work in US national security, don't try to have the applied math of applied optimization for a career. Don't spend a lot of time studying optimization.
Later might be able to be the founder, COB, CEO of a startup where some math is a big advantage.
Work backwards, check those jobs exist, look at what qualifications they'd benefit from
Thanks for investing so much time to it, I share your sadness for your wife and hope you get ao much good as you tried to bring to the world, man
I was naive, manipulated, and fooled. Now on the OP, there is a book title with "Applied Optimization", and I'm outraged.
So: "Always look for the hidden agenda."
The objective of the game is to figure out what kind of planets are hidden in sector of the boards using clues like: "There are 2 comets between secotr 3 and 7" or "No comet is next to an asteroid ".
Sketching the solver was incredibly fun and rewarding!
The original posting is about new tools and algorithms, with some more analysis. Well beyond my background from undergrad courses in LP and OR, but probably more relevant and insightful to you.
[0] https://news.ycombinator.com/item?id=41609670
For example all of the "hard" leetcode problems can be casted as math programming ones. But the interviewers will not appreciate this solution approach lol.
Once you conquer the logic/language then learning the tools is the easy part.
I once witnessed a programmer with a PhD in Maths find closed form formulas for a lot of questions where it was expected to write some code with loops building/accumulating a result. As a simple example, to explain what was going on, if the question would be "calculate the 100th fibonacci number", she would just use Binet's formula to do so (as opposed to using a loop). I was rather impressed how often that happened.
If they’re writing a compartmentalized library specific to their domain, it’s fine. I’ve worked with a Stats PhD doing that.
If you’re dropping them into a shared codebase, the comprehensibility of their code to the other people on their team is essential. Great code that depends on knowledge no one else on the team has is not great. You end up with “That’s going to take forever to change, Steve wrote it”.
„Learning how to formulate problems as integer/linear programming ones“, as another commenter put it, works great if it‘s a natural fit and sure is fun for idk 7th grade math text problems I guess but OTOH squeezing realistic problems into systems of hundreds of equations (or more if dealing with linearizations of inherently non-linear/concave/multi-step problems) to satisfy tool idiosyncracies calls for additional tools in your arsenal.
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