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A first-order primal-dual method with adaptivity to local smoothness [article]

Maria-Luiza Vladarean, Yura Malitsky, Volkan Cevher
2021 arXiv   pre-print
Furthermore, when f is also locally strongly convex and A has full row rank we show that our method converges with a linear rate.  ...  We propose an adaptive version of the Condat-Vũ algorithm, which alternates between primal gradient steps and dual proximal steps.  ...  Acknowledgements The first author is grateful to Ya-Ping Hsieh for his feedback on the manuscript and for helpful research discussions throughout the development of this work.  ... 
arXiv:2110.15148v1 fatcat:knhloajgwzgxxneyu65bcyt7uy

Getting Feasible Variable Estimates from Infeasible Ones: MRF Local Polytope Study

Bogdan Savchynskyy, Stefan Schmidt
2013 2013 IEEE International Conference on Computer Vision Workshops  
Whereas the infeasible primal estimates can typically be produced from (sub-)gradients of the dual function, it is often not easy to project them to the primal feasible set, since the projection itself  ...  We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and discuss its advantages over existing methods.  ...  Prox-Point Primal-Dual Algorithms (First-Order Primal-Dual, ADMM, ADLP).  ... 
doi:10.1109/iccvw.2013.43 dblp:conf/iccvw/Savchynskyy013 fatcat:gi4momhiefdtncmjvk3xs23one

Error estimation and mesh adaptation for Signorini–Coulomb problems using E-FEM

François Kuss, Frédéric Lebon
2011 Computers & structures  
or remeshing in order to analyse the local errors with a view to determining appropriated mesh sizes for obtaining an overall target error.  ...  Improving the solution by performing adaptive remeshing As mentioned above the aim of remeshing is to perform an initial calculation on an initial mesh in order to determine a topology of local errors,  ... 
doi:10.1016/j.compstruc.2010.11.001 fatcat:b5xgkjcmgjcdvkjlg5g7mqryi4

Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study [article]

Bogdan Savchynskyy, Stefan Schmidt
2012 arXiv   pre-print
This paper proposes a method for construction of approximate feasible primal solutions from dual ones for large-scale optimization problems possessing certain separability properties.  ...  We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and demonstrate its superiority over existing methods.  ...  For the experiments we employ our own implementations of the First Order Primal Dual Algorithm (acronym FPD) as described by , the adaptive diminishing smoothing algorithm ADSAL proposed by , the dual  ... 
arXiv:1210.4081v1 fatcat:kuktgtt6wjgpjoya3zo2a4dcee

An Adaptive Penalty Method for Inequality Constrained Minimization Problems

Wietse M. Boon, Jan M. Nordbotten
2019 European Conference on Numerical Mathematics and Advanced Applications  
The primal-dual active set method is observed to be the limit of a sequence of penalty formulations.  ...  to the active set method.  ...  This work forms a link between these two families by proposing a penalty method that adaptively evolves to the primal-dual active set method.  ... 
doi:10.1007/978-3-030-55874-1_14 dblp:conf/enumath/BoonN19 fatcat:3jmdgf2qyzghpa7pfgal5qleqq

Condition Number and Clustering-Based Efficiency Improvement of Reduced-Order Solvers for Contact Problems Using Lagrange Multipliers

Simon Le Berre, Isabelle Ramière, Jules Fauque, David Ryckelynck
2022 Mathematics  
A clustering strategy on the parametric space is then proposed in order to deal with piece-wise low-rank approximations.  ...  On each cluster, a local accurate hyper-reduced model is built thanks to the enrichment strategies.  ...  A local RID is built for each local model. As previously, a DEIM on the primal RB and a contribution from a DEIM on a dual POD RB (with a threshold = 10 −6 ) is used to obtain the set of nodes L.  ... 
doi:10.3390/math10091495 fatcat:7raduzqzrbeo5nq7oltcayjxg4

3D Adaptive Central Schemes: part I Algorithms for Assembling the Dual Mesh [article]

Sebastian Noelle, Wolfram Rosenbaum, Martin Rumpf
2015 arXiv   pre-print
Here we start with an adaptively refined cartesian primal grid in 3D and present a construction technique for the staggered dual grid based on L^∞-Voronoi cells.  ...  The local refinement constellation on the primal grid leads to a finite number of uniquely defined local patterns on a primal cell. Assembling adjacent local patterns forms the dual grid.  ...  Though up to now only first order, the extension of the staggered grid approach to a higher order 3D finite volume scheme is in process.  ... 
arXiv:1501.03614v1 fatcat:vf4frmujkvgcdohkz6d54xl5zu

Stochastic Coordinate Descent Methods for Regularized Smooth and Nonsmooth Losses [chapter]

Qing Tao, Kang Kong, Dejun Chu, Gaowei Wu
2012 Lecture Notes in Computer Science  
In particular, we first present a principled and practical SCD algorithm for regularized smooth losses, in which the one-variable subproblem is solved using the proximal gradient method and the adaptive  ...  When the loss is nonsmooth, we present a novel SCD algorithm, in which the one-variable subproblem is solved using the dual averaging method.  ...  Acknowledgments The work was supported in part by the NSFC (Grant No. 60835002, 60975040 and 61175050) and the first author is also supported by the Open Project Program of the NLPR.  ... 
doi:10.1007/978-3-642-33460-3_40 fatcat:oj35t52xtvh6pj4do77d7h7ltq

A Deep Primal-Dual Network for Guided Depth Super-Resolution [article]

Gernot Riegler, David Ferstl, Matthias Rüther, Horst Bischof
2016 arXiv   pre-print
We combine a deep fully convolutional network with a non-local variational method in a deep primal-dual network.  ...  By unrolling the optimization steps of a first-order primal-dual algorithm and formulating it as a network, we can train our joint method end-to-end.  ...  In the PDN we unroll the optimization procedure of a non-local variational model, namely of the first-order primal-dual algorithm [3] .  ... 
arXiv:1607.08569v1 fatcat:hqxhkgtjl5cplmpn2sqpdvfo3m

Robust Poisson Surface Reconstruction [chapter]

Virginia Estellers, Michael Scott, Kevin Tew, Stefano Soatto
2015 Lecture Notes in Computer Science  
We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator function of  ...  For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface.  ...  We choose a first-order method because the size of the problem makes second-order methods unfeasible.  ... 
doi:10.1007/978-3-319-18461-6_42 fatcat:pzsopmei65fxtpscaxwulvyx4m

Unsupervised saliency estimation based on robust hypotheses

Fei Xu, Min Xian, H. D. Cheng, Jianrui Ding, Yingtao Zhang
2016 2016 IEEE Winter Conference on Applications of Computer Vision (WACV)  
The primal-dual interior point method is applied to optimize the proposed QP in polynomial time.  ...  First, we propose an adaptive center-based bias hypothesis to replace the most common image center-based center-bias.  ...  optimization We formulate the visual saliency estimation as a QP problem with linear equality and inequality constraints, and the primal-dual method can be applied to optimize the problem globally.  ... 
doi:10.1109/wacv.2016.7477623 dblp:conf/wacv/XuXCDZ16 fatcat:hz7ofjyxl5e3lmfc6wauqtttly

Multiscale Kernel Smoothing Using A Lifting Scheme

Christophe Damerval, Maarten Jansen
2009 Zenodo  
In order to enhance the number of dual vanishing moments (thereby creating more sparsity and better compressibility), one could replace the kernel smoothing by a more advanced local polynomial smoothing  ...  In order to evaluate our method, we compare it with related lifting schemes on for irregular point sets.  ... 
doi:10.5281/zenodo.41389 fatcat:qllhwok5unchjchazvq3axkkxm

Multiscale Local Polynomial Smoothing in a Lifted Pyramid for Non-Equispaced Data

Maarten Jansen
2013 IEEE Transactions on Signal Processing  
The design of these decomposition requires pairs of non-stationary filters, adapted to each other and to the locations of the observations at hand.  ...  Thanks to the slight redundancy and to the smoothing operations in the lifting scheme, the proposed construction unifies sparsity of the analysis, smoothness of the reconstruction and stability of the  ...  on one hand and linear interpolating prediction on the other hand, both methods equipped with a two-taps update for local primal vanishing moments.  ... 
doi:10.1109/tsp.2012.2225059 fatcat:e6b5l27hyjeuplaz3htpu2ojny

A study of Nesterov's scheme for Lagrangian decomposition and MAP labeling

Bogdan Savchynskyy, Jorg Kappes, Stefan Schmidt, Christoph Schnorr
2011 CVPR 2011  
We show that in order to obtain an efficiently convergent iteration, this approach should be augmented with a dynamic estimation of a corresponding Lipschitz constant, leading to a runtime complexity of  ...  In this paper, we focus specifically on Nesterov's optimal first-order optimization scheme for nonsmooth convex programs, that has been studied for a range of other problems in computer vision and machine  ...  Smoothing selection Next we compare Nesterov's method with fixed smoothing to a method with adaptive smoothing for the same precision. In the first case, precision is selected according to (17) .  ... 
doi:10.1109/cvpr.2011.5995652 dblp:conf/cvpr/SavchynskyyKSS11 fatcat:z3fgazxkbzevpbvqbxooheqqie

Smooth and Strong: MAP Inference with Linear Convergence

Ofer Meshi, Mehrdad Mahdavi, Alexander G. Schwing
2015 Neural Information Processing Systems  
However, optimization of the resulting program is in general challenging due to non-smoothness and complex non-separable constraints.  ...  Specifically, we introduce strong convexity by adding a quadratic term to the LP relaxation objective.  ...  To remedy this shortcoming, it has been proposed to smooth the objective by replacing the local maximization with a soft-max [7, 8] .  ... 
dblp:conf/nips/MeshiMS15 fatcat:n4abrdbmlrez7lyyxpqajtng3y
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