Question

QE: Find the local minimum of f(x)=x - k*Ln(x), for constant k>0. This is related to “interior point methods” in optimization algorithms (which I teach about in Math 560). It’s a way of saying “minimize f(x)=x for x>=0” without having a separate constraint like “x>=0”; it turns a minimum-is-at-an-endpoint kind of problem into a minimum-is-in-the-interior-of-the-interval problem. This is handy if you have more than one dimension and finding the cornerpoints would take too long.On the other hand, it turns a linear problem (with constraints) into a nonlinear problem, which for decades seemed like a bad trade-off to algorithm designers, but turns out it can be a good idea.

Answer 1

Giren finchion, n(x) 2 K find csihical paip TO f'cx) K 2 Naw, Secwe deva te K 2 f'(K) K K2 Kis posinie 1 2 hoo local mninima fca At

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