Local convergence of proximal splitting methods for rank constrained problems
C Grussler, P Giselsson - 2017 IEEE 56th Annual Conference …, 2017 - ieeexplore.ieee.org
2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017•ieeexplore.ieee.org
We analyze the local convergence of proximal splitting algorithms to solve optimization
problems that are convex besides a rank constraint. For this, we show conditions under
which the proximal operator of a function involving the rank constraint is locally identical to
the proximal operator of its convex envelope, hence implying local convergence. The
conditions imply that the non-convex algorithms locally converge to a solution whenever a
convex relaxation involving the convex envelope can be expected to solve the non-convex …
problems that are convex besides a rank constraint. For this, we show conditions under
which the proximal operator of a function involving the rank constraint is locally identical to
the proximal operator of its convex envelope, hence implying local convergence. The
conditions imply that the non-convex algorithms locally converge to a solution whenever a
convex relaxation involving the convex envelope can be expected to solve the non-convex …
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hence implying local convergence. The conditions imply that the non-convex algorithms locally converge to a solution whenever a convex relaxation involving the convex envelope can be expected to solve the non-convex problem.
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