Question: The proximal operator of the function g is the mapping prox, : R - R given by prox, (z ) = arg min llac -

The proximal operator of the function g is the mapping prox, : R" - R" given by prox, (z ) = arg min llac - z|12 + g(ac). CERn For each of the following functions, find the expressions for their proximal operators. (a) g1(x) = c, where c E R. (b) g2(x) = axc + b, where a E R" and b E R. (c) g3(x) = >x Qx, where Q E Rnxn is a symmetric positive semidefinite matrix

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