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Convex Optimization by Lieven Vandenberghe, Stephen Boyd

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Example 3.33  Distance ratio function. Suppose a, b Rn, and define

i.e., the ratio of the Euclidean distance to a to the distance to b. Then f is quasiconvex on the halfspace {x | x a 2 x b 2}. To see this, we consider the α-sublevel set of ...

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