A version of the so called (convex) trust region problem amounts to finding the minimum of a convex quadratic function over an Euclidean ball, that is where is the given radius of the ball Prove that the optimal solution to this problem is unique and it is given by where or otherwise l is the unique value such that min xHx cx d x xTx r, s t

Question: A version of the so-called (convex) trust-region problem amounts to finding the minimum of a convex quadratic function over an Euclidean ball, that is where

A version of the so-called (convex) trust-region problem amounts to finding the minimum of a convex quadratic function over an Euclidean ball, that is

min xHx+cx+d x xTx r, s.t.:

where is the given radius of the ball. Prove that the optimal solution to this problem is unique and it is given by

whereor otherwise l is the unique value such that

min xHx+cx+d x xTx r, s.t.:

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