A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
Matrix computations (3rd ed.)
Convex Optimization
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
A study of Nesterov's scheme for Lagrangian decomposition and MAP labeling
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
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We investigate the First-Order Primal-Dual (FPD) algorithm of Chambolle and Pock [1] in connection with MAP inference for general discrete graphical models. We provide a tight analytical upper bound of the stepsize parameter as a function of the underlying graphical structure (number of states, graph connectivity) and thus insight into the dependency of the convergence rate on the problem structure. Furthermore, we provide a method to compute efficiently primal and dual feasible solutions as part of the FPD iteration, which allows to obtain a sound termination criterion based on the primal-dual gap. An experimental comparison with Nesterov's first-order method in connection with dual decomposition shows superiority of the latter one in optimizing the dual problem. However due to the direct optimization of the primal bound, for small-sized (e.g. 20×20 grid graphs) problems with a large number of states, FPD iterations lead to faster improvement of the primal bound and a resulting faster overall convergence.