Learned Primal-Dual Reconstruction

Learned Primal-dual Reconstruction

We propose the Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization method, but where the proximal operators have been replaced with convolutional neural networks. The algorithm is trained end-to-end, working directly from raw measured data and i...

Primal - Dual Kernel

Primal-Dual Combinatorial Algorithms

Linear program and its duality have long been ubiquitous tools for analyzing NP-hard problems and designing fast approximation algorithms. Plotkin et al proposed a primaldual combinatorial algorithm based on linear duality for fractional packing and covering, which achieves significant speedup on a wide range of problems including multicommodity flow. The key ideas there are: 1) design a primal...

The Primal - dual Algorithm

As we have seen before, using strong duality, we know that the optimum value for the following two linear programming are equal, i.e. u = w, if they are both feasible. u = max{cx : Ax ≤ b, x ≥ 0} (P ) w = min{b y : A y ≥ c, y ≥ 0} (D) Using the above result, we can check the optimality of a primal and/or a dual solution. Theorem 1. Suppose x and y are feasible solutions to (P ) and (D). Then x ...

Dual-Primal FETI Method

The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioner was shown to be numerically scalable for second order elasticity problems while the two level...