The set

x^5/3 <= t, x,t>=0.0

can be represented by

x^2 <= 2 s t, s,t >= 0,

u = x,

v = s,

z = v,

z^2 <= 2fg, f,g > = 0,

f = 0.5,

4 g = h,

h^2 <= 2uv, u,v >= 0.

I will leave it to reader to verify it is correct.

this particular set I have come up over again and again in financial applications. I suppose it has something to do with modeling of transactions costs.

An obvious question is why replace a simple problem but something that looks quite a bit complicated.

However, both in theory and practice the conic quadratic optimization problems is easier to solve then general convex problems.

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