Diagonal preconditioning for first order primal-dual algorithms in convex optimization

By Thomas Pock, Antonin Chambolle. Vision, 2011

524 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1c2707f677cef1883e44141efdda643c86a20586

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In Computational Mechanics

In Computational Theory and Mathematics

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Citations in the corpus

A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model (2013, methodology): “(2009) with step sizes chosen according (Pock and Chambolle 2011).”
A Rewriting System for Convex Optimization Problems (2017, methodology): “One scaling technique, called diagonal preconditioning, premultiplies such constraints by diagonal matrices and also changes variables by premultiplying the optimization variable by another diagonal matrix (Kelley, 1995, § 2.5; Pock & Chambolle, 2011; Takapoui & Javadi, 2016).”
Segment based 3D object shape priors (2015, methodology): “1 is minimized with the first order primaldual algorithm [20].”
Image Guided Depth Upsampling Using Anisotropic Total Generalized Variation (2013, methodology): “In practice the relaxation parameter θ is updated in every iteration, according to [2], and the optimal step sizes are calculated using preconditioning, as proposed in [17].”
A Primer on Monotone Operator Methods (2015, methodology): “Choosing E well and applying the algorithm to the transformed problem can improve the performance [51,58,59,96,97,105].”
OSQP: an operator splitting solver for quadratic programs (2017, unknown): “5], [11,44,46,47,79].”
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding (2013, background): “The scaling parameters E, D, σ, and ρ can be chosen to (approximately) achieve this [64,68,71], though the question of whether there is an optimal scaling remains open.”
Generalized Connectivity Constraints for Spatio-temporal 3D Reconstruction (2014, methodology): “This saddle point problem is optimized using the preconditioned primal-dual algorithm by Pock and Chambolle [23].”
Simultaneous Optical Flow and Intensity Estimation from an Event Camera (2016, methodology): “Their respective resolvent operators are defined as in [17].”
A Symmetry Prior for Convex Variational 3D Reconstruction (2016, methodology): “As a result, all three terms of the functional are convex and we can eﬃciently minimize energy (3) with the pre-conditioned ﬁrst-order primal-dual algorithm [21].”
An introduction to continuous optimization for imaging (2016, methodology): “A simpler approach is suggested in Pock and Chambolle (2011), for problems where a diagonal preconditioning does not alter the property that the proximal operators of f and g are easy to compute.”
Class Specific 3D Object Shape Priors Using Surface Normals (2014, methodology): “For the optimization we use the preconditioned first order primal-dual algorithm presented in [14].”
iPiano: Inertial Proximal Algorithm for Nonconvex Optimization (2014, methodology): “We additionally accelerate the SPD algorithm used in the previous work [24] by applying the diagonal preconditioning technique [37], which significantly reduces the required iterations for the primal-dual algorithm in the inner loop.”
Dense Semantic 3D Reconstruction (2017, unknown): “[29], and introduce Lagrange multipliers, ns for the constraints P i x i s 1⁄4 1, ð s!Þk for xs 1⁄4 P jðx s Þk and ð is Þk for xs 1⁄4 P jðx s ekÞk, 8k 2 f1; 2; 3g, corresponding to the three coordinate axes.”
Semantic 3D Reconstruction with Continuous Regularization and Ray Potentials Using a Visibility Consistency Constraint (2016, methodology): “Minimization step The primal-dual algorithm [24] is run on the surrogate convex program for a fixed number of p iterations.”
An Inertial Forward-Backward Algorithm for Monotone Inclusions (2014, unknown): “In the context of saddle point problems, Pock and Chambolle [42] proposed a preconditioning of the form”
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm (2011, background): “[34], which appears to perform efficiently for small λ.”