Bregman projection
$begingroup$
Given a convex body $K$ and a point $y$ outside the convex body (in the ambient space), the Bregman projection of $y$ , with respect to the regularizer $R$, is defined as
$x=rm{argmin}{B_{R}left(omega, yright):omega in K}$
where, $B_{R}left(omega, yright)=Rleft(omegaright)+Rleft(yright)-nabla Rleft(yright)'left(omega-yright)$
Then how can I show the following
$[nabla R(x) − nabla R(y)]' (omega − x) >0$
Please give me some hint.
self-learning divergence
edited Jan 7 at 9:17
Bernard
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
$endgroup$
add a comment |
$begingroup$
Given a convex body $K$ and a point $y$ outside the convex body (in the ambient space), the Bregman projection of $y$ , with respect to the regularizer $R$, is defined as
$x=rm{argmin}{B_{R}left(omega, yright):omega in K}$
where, $B_{R}left(omega, yright)=Rleft(omegaright)+Rleft(yright)-nabla Rleft(yright)'left(omega-yright)$
Then how can I show the following
$[nabla R(x) − nabla R(y)]' (omega − x) >0$
Please give me some hint.
self-learning divergence
edited Jan 7 at 9:17
Bernard
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
$endgroup$
add a comment |
$begingroup$
Given a convex body $K$ and a point $y$ outside the convex body (in the ambient space), the Bregman projection of $y$ , with respect to the regularizer $R$, is defined as
$x=rm{argmin}{B_{R}left(omega, yright):omega in K}$
where, $B_{R}left(omega, yright)=Rleft(omegaright)+Rleft(yright)-nabla Rleft(yright)'left(omega-yright)$
Then how can I show the following
$[nabla R(x) − nabla R(y)]' (omega − x) >0$
Please give me some hint.
self-learning divergence
edited Jan 7 at 9:17
Bernard
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
$endgroup$
Given a convex body $K$ and a point $y$ outside the convex body (in the ambient space), the Bregman projection of $y$ , with respect to the regularizer $R$, is defined as
$x=rm{argmin}{B_{R}left(omega, yright):omega in K}$
where, $B_{R}left(omega, yright)=Rleft(omegaright)+Rleft(yright)-nabla Rleft(yright)'left(omega-yright)$
Then how can I show the following
$[nabla R(x) − nabla R(y)]' (omega − x) >0$
Please give me some hint.
self-learning divergence
self-learning divergence
edited Jan 7 at 9:17
Bernard
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
edited Jan 7 at 9:17
Bernard
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
edited Jan 7 at 9:17
Bernard
123k741117
edited Jan 7 at 9:17
Bernard
123k741117
edited Jan 7 at 9:17
Bernard
123k741117
123k741117
asked Jan 7 at 8:40
Shefali royShefali roy
93
asked Jan 7 at 8:40
Shefali royShefali roy
93
asked Jan 7 at 8:40
Shefali royShefali roy
93
93
add a comment |
add a comment |
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