Infimal-convolution dual subgradients
= Infimal-convolution dual subgradients
{title2=$\partial(h\square k)(z)=\arg\max_p\{\langle p,z\rangle-h^*(p)-k^*(p)\}$}
Under the finite-valued assumptions, <subgradients> of an <infimal convolution> are obtained as its attained dual optimizers. Equivalently $z\in\partial(h^*+k^*)(p)$. Splitting the latter <subdifferential> into two separate ones needs a <subdifferential sum rule> qualification; solving the aggregate dual objective avoids that extra assumption.