Can someone give some examples of convex functions with positive semi-definite Hessian, where the Hessian is non-continuous everywhere?
2026-03-29 00:06:28.1774742788
Convex function with rapidly changing Hessian, or non-continuous Hessian
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How about for example:
$$ f(x) = \mathbf 1_{x\le 0} {x^2\over 2} + \mathbf 1_{x\ge 0} x^2 $$
blue line is the function, green is gradient, red is hessian. I think it meets your requirements.