Question: Let X R n + m be a matrix with non-negative entries, and p, r [1, + ], with p r. We

Let X ∈ Rn+m be a matrix with non-negative entries, and p, r ∈  [1, + ∞], with p ≥ r. We consider the problem


Ppr (X) = max ||XV||||||p 1. V

1. Show that the function fX : Rm+ → R, with values

is concave when p ≥ r.

2. Use the previous result to formulate an efficiently solvable convex problem that has Φp,r(X)r as optimal value.

Ppr (X) = max ||XV||||||p 1. V

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