Convex optimization & euclidean distance geometry

  • Is the Euclidean distance convex?

    Squared Euclidean distance does not form a metric space, as it does not satisfy the triangle inequality.
    However it is a smooth, strictly convex function of the two points, unlike the distance, which is non-smooth (near pairs of equal points) and convex but not strictly convex..

What is the relationship between convex sets and convex functions?

Geometry of Convex Functions The link between convex sets and convex functions is via the epigraph: A function is convex if and only if its epigraph is a convex set

We limit our treatment of multidimensional functions3

1 to finite-dimensional Euclidean space


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