How to specify the variables to be integers in fmincon function.

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Zejun Xiang 2016-10-27

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评论： Math Works 2022-7-29

I need to solve a quadratically constrained program by fmincon with all variables restricted in integers. Is it possible to specify variable types in fmincon? If not, is there another way to solve this problem?

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John D'Errico 2016-10-27

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You cannot do so. Period. fmincon does not allow integer constraints. To solve that class of problem, you need a integer programming tool, in this case, a nonlinear one. But NOT fmincon.

I believe the genetic optimization tools can allow integer constraints.

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Walter Roberson 2016-10-27

ga() allows integer constraints, but when you have an integer constraint it does not allow nonlinear constraints.

Abdolkarim Mohammadi 2019-8-14

When you have integer variables in ga(), you can have linear and/or nonlinear inequality constraints. Integer ga() only prohibits linear and/or nonlinear equality constraints.

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Math Works 2022-7-28

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Is there an equivalent integer one that doesn't define f as vectors?

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Walter Roberson 2022-7-28

Then you need function overloading to handle it internally using a different method.

No, you need completely different algorithms, with there being no known feasible solutions for even relatively simple situations. "feasible" meaning "substantially faster than just trying all of the possibilities."

Example: suppose you have a container that can hold 12 L, and you have items that are 1, 2, 5, and 8 L, and the task is to pack a subset of the items into the container, coming as close to filling it up as possible without overflowing. With continuous mathematics you just say, "That's easy, take 1 1/2 of the 8 L items". With discrete mathematics you need to run through most of the combinations to arrive at solutions such as 2 of the 5L and 1 of the 2L. This particular problem is not difficult, but in this class of problems, one of the better algorithms is

-- exponential time in the number of items.

Integer optimization problems include topics in Public Key Encryption, discrete logarithms, elliptical curve encryption, proof of Fermat's Last Theorem... very tricky stuff.

Walter Roberson 2022-7-29

Yes, you generate a set of integers, and then you treat those as locally constant and optimize over the other values. You get a best result for varying the other variables relative to that particular list of integers, and then you move on to the next list of integers, and repeat, keeping track of the best result as you go.

Math Works 2022-7-29

Yes, that's exactly what I did.

Basically, every for-chain iteration step treats all the integer variables as constants, then do the local continuous constrained optimization problem. With some global tracker variables and helper functions, this can be implemented with some effort.

I still don't understand why MATLAB can't abstract this process though. Just ask for the boundries for the integer variables. Formulating the problem becomes harder when you need to think about the lower level implementations. At that point, I'm better off doing it in C++ directly.

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