# Are these valid optimization programs?

I had some ideas for optimization programs, but I'm not sure if I'm off in wonderland. :)

The first one is:

## x, y, z are integers > 0

Here h is the length of the hypotenuse of a Pythagorean triad, this minimization program is for finding the next highest value Pythagorean triad. The idea is that running this program over and over would give a series of Pythagorean triads.

The next program is:

## a, b are integers > 0

The idea here is to show somehow that this minimisation program violates some convex optimisation feasibility condition. This would prove that √2 is not a rational number. I call this method of proof: "proof by infeasibility." XD

The next program combines the first two in an obvious way:

## x, y, z are integers > 0

If it’s possible to show that this minimisation program violates some convex optimisation feasibility condition for values of n ≥ 3, i.e. the program is infeasible, then this would hopefully prove Fermat’s last theorem.

And the last program is an attempt to frame the Riemann hypothesis as an optimization program. If this method of doing things isn’t a crackpot way of doing things then maybe it would be possible to show that the non-trivial zeros of the Riemann zeta function are only feasible on the line s = ½ + ei.

## ξ(s) = 0

Here s = b + di is a known non-trivial zero of the Riemann zeta function, and s = a + ci is the next non-trivial solution to Riemann’s zeros. We don’t need to actually find the next solution, we just need to show that for any non-trivial solution of Riemann’s zeros which lies on the line s = ½ + ei, the feasible region for this program strictly lies on the same line. This would be like a proof by induction.

Unfortunately, complex numbers are unordered, so I'm not sure if optimizing complex functions is possible... But I'm not sure about most of this stuff. :)

Chickenmales
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