Primal and Dual Access

Primal-Dual Rates and Certificates

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in particular in machine learning applications. We obtain new primal-dual convergence rates e.g. for the Lasso as well as many L1, Elastic-Net and group-lasso-r...

Primal and dual assignment networks

This paper presents two recurrent neural networks for solving the assignment problem. Simplifying the architecture of a recurrent neural network based on the primal assignment problem, the first recurrent neural network, called the primal assignment network, has less complex connectivity than its predecessor. The second recurrent neural network, called the dual assignment network, based on the ...

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...