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John D'Errico
John D'Errico
最後のアクティビティ: 2022 年 11 月 10 日

linprog failed to work. why? Did I do something wrong?

I've now seen linear programming questions pop up on Answers recently, with some common failure modes for linprog that people seem not to understand.
One basic failure mode is an infeasible problem. What does this mean, and can it be resolved?
The most common failure mode seems to be a unbounded problem. What does this mean? How can it be avoided/solved/fixed? Is there some direction I can move where the objective obviously grows without bounds towards +/- inf?
Finally, I also see questions where someone wants the tool to produce all possible solutions.
A truly good exposition about linear programming would probably result in a complete course on the subject, and Aswers is limited in how much I can write (plus I'll only have a finite amount of energy to keep writing.) I'll try to answer each sub-question as separate answers, but if someone else would like to offer their own take, feel free to do so as an answer, since it has been many years for me since I learned linear programming.