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A general framework for solving convex optimization problems involving the sum of three convex functions. (arXiv:1705.06164v1 [math.OC])
来源于:arXiv
In this paper, we consider solving a class of convex optimization problem
which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where
$f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and
$h(x)$ have closed-form expression of their proximity operators and $B$ is a
bounded linear operator. This type of optimization problem has wide application
in signal and image processing. To make full use of the differentiability
function in the optimization problem, we take advantage of two operator
splitting methods: the forward backward splitting method and the three operator
splitting method. In the iteration scheme derived from the two operator
splitting methods, we need to compute the proximity operator of $g+h \circ B$
and $h \circ B$, respectively. Although these proximity operators don't have a
closed-form solution, they can be solved very effectively. We mainly employ two
different approaches to solving these proximity operators: one is dual and the
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