You haven't said what the lower and upper constraints look like. If they are parametrized nicely you can use a variant of what's called the Kelley cutting plane method. Basically, the idea is that at every stage you have a small finite set of "active" constraints. You find a feasible solution (i.e. one satisfying all the constraints). If upper and lower have a nice structure you can find some of the inactive constraints that are maximally violated, and add those, etc. Victor On Fri, Oct 11, 2019 at 2:52 PM Mike Stay <metaweta@gmail.com> wrote:
I'd like to efficiently find solutions to constraints of the form
lower1 <= ((x * 0x000001) mod 2^24) < upper1 && lower2 <= ((x * 0x088405) mod 2^24) < upper2 && lower3 <= ((x * 0x652819) mod 2^24) < upper3 && ... where the constants are consecutive powers of 0x088405. Brute-forcing the space isn't much work to do for a single set of upper and lower bounds, but when I've got 2^40 such sets, it's daunting.
Any ideas? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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