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Applied Mathematical Programming (1977)

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Re: Applied Mathematical Programming (1977)

#11

Post by wheelinsupial »

6gvONxR4sf7o wrote: post #2

Has this been updated since 1977? Because the field and tools and even the view points have changed a ton.

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.

[0] https://news.ycombinator.com/item?id=41609670

Re: Applied Mathematical Programming (1977)

#12

Post by hyperthesis »

toolslive wrote: post #9
whatever1 wrote: post #7

Earlier quoted context omitted.

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 approac…

> 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 op…

TBF Binet's formula is astonishing

Re: Applied Mathematical Programming (1977)

#14

Post by wenc »

npalli wrote: post #5

This is from 1977. I suppose it's ok for fundamentals but you can probably do better going with a modern text like Model Building in Mathematical Programming by H. Paul Williams (5th Edition)

H. P. Williams' book is often recommended for learning MIP formulations.

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.

Re: Applied Mathematical Programming (1977)

#15

Post by contravariant »

hyperthesis wrote: post #12
toolslive wrote: post #9

Earlier quoted context omitted.

> 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 op…

TBF Binet's formula is astonishing

If you think it is you should read up on linear algebra, specifically its use in finite difference equations and how that relates to linear differential equations.

The astonishment doesn't get less, but it shifts from Binet's single formula to the exponential map, and maybe the fundamental theorem of algebra (or generalisations).

Re: Applied Mathematical Programming (1977)

#16

Post by LegionMammal978 »

toolslive wrote: post #9
whatever1 wrote: post #7

Earlier quoted context omitted.

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 approac…

> 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 op…

Is Binet's formula really that practical a way to calculate the Fibonacci numbers (except asymptotically)? The problem is, you have this nice clean expression, but you'd still have to implement a bunch of fancy arbitrary-precision arithmetic to approximate the golden ratio through Newton's method. In other words, the formula gives much more information about the structure of the Fibonacci numbers than their actual values.

For evaluating the Fibonacci numbers (as with any other integer linear recurrence), I'd generally prefer the matrix-exponentiation-by-squaring approach, or one of the simplified formulas based on it. Those don't need anything more complicated than bigint multiplication. [And from there, taking the ratio between two values gives you a quick way to approximate the golden ratio!]

Re: Applied Mathematical Programming (1977)

#17

Post by travisjungroth »

whatever1 wrote: post #7
6gvONxR4sf7o wrote: post #2

Has this been updated since 1977? Because the field and tools and even the view points have changed a ton.

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 approac…

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”.

Re: Applied Mathematical Programming (1977)

#18

Post by fn-mote »

LegionMammal978 wrote: post #16
toolslive wrote: post #9

Earlier quoted context omitted.

> 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 op…

Is Binet's formula really that practical a way to calculate the Fibonacci numbers (except asymptotically)? The problem is, you have this nice clean expression, but you'd still have to implement a bunch of fancy arbitrary-precision arithmetic to approximate the golden ratio through Newton's method. In other words, the formula gives much more information about the structure of the Fibonacci numbers than their actual va…

Once you have postulated BigInt as available, the mathematician is going to make a rational approximation for phi using the continued fraction expansion that they know by heart (because of its “simplicity”).

Re: Applied Mathematical Programming (1977)

#19

Post by graycat »

"Applied ..."?

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.

Re: Applied Mathematical Programming (1977)

#20

Post by whiterknight »

graycat wrote: post #19

"Applied ..."? 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. Som…

You’re attributing these life challenges to your STEM PhD speciality?

I am sensitive to your hardship, but optimization has nothing to do with it. People are succeeding with bachelor’s degrees in Latin.

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