Facilitating OWL norm minimizations

We present some characterizations of the ordered weighted $$\ell _1$$ ℓ 1 norm (aka sorted $$\ell _1$$ ℓ 1 norm) and of the vector Ky-Fan norm as solutions to linear programs involving reasonably many variables and constraints. Such linear characterizations can be exploited to recast and effortlessly solve a variety of convex optimization problems involving these norms. Similar linear characterizations are given for the dual norms of the ordered weighted $$\ell _1$$ ℓ 1 norm and the Ky-Fan norm.

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