We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. More…
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48 results for “Dual Augmented Lagrangian”
Method solves nonconvex constrained optimization problems with a new augmented Lagrangian approach.
problem Nonconvex composite functional constraints with inequality constraints.
method First-order augmented Lagrangian method with smoothed prox-linear reformulation.
result Explicit convergence rates for the proposed method in terms of KKT residual.
Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimationstat.ML
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymp…
Cancellation-Free Regret Bounds for Lagrangian Approaches in Constrained Markov Decision Processescs.LG
New algorithm reduces regret in CMDPs without cancellation of errors.
problem Lagrangian approaches in CMDPs struggle with cancellation of errors.
method OptAug-CMDP, based on augmented Lagrangian method.
result Regret of for both objective and constraint violation.
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
A sparse semismooth Newton based augmented Lagrangian method for large-scale support vector machinesmath.OC
Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However, the numerical difficulties of the SVMs will become severe with the increase of t…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…
A new algorithm efficiently selects features for functional data classification.
problem Feature selection and classification of functional data in high-dimensional spaces.
method Developed a novel optimization problem integrating logistic loss and functional features. Employed functional principal components and a new adaptive Dual Augmented Lagrangian algorithm for efficient minimization.
result FSFC outperforms other methods in computational time and classification accuracy.
We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of nonconvex -smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into subproblems, and utilizes an augmented Lagrangian b…
A new method solves complex constrained minimax problems.
problem Solving constrained minimax optimization problems.
method First-order augmented Lagrangian method.
result Established an operation complexity of .
For a Legendrian torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed exact Lagrangian fillings, where is the -th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we com…
To a Legendrian knot, one can associate an category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomolog…
A new algorithm solves the metric nearness problem efficiently.
problem Finding the nearest distance matrix that satisfies triangle inequalities.
method Delayed constraint generation with semismooth Newton based proximal augmented Lagrangian method (PALM).
result Solves problems with up to 10^8 variables and 10^13 constraints efficiently.
Study of Legendrian links using Floer theory and cluster varieties.
problem Understanding exact Lagrangian fillings of positive braid Legendrian links.
method Floer-theoretic approach and exact Lagrangian cobordisms.
result Proves that positive braid Legendrian links admit infinitely many exact Lagrangian fillings.
A new method tackles nonconvex optimization with penalties and proximal terms.
problem Nonconvex optimization problems with equality and inequality constraints.
method Inexact proximal augmented Lagrangian method (P-ALM) with adaptive penalty and proximal parameters.
result Effective convergence properties and numerical superiority over traditional methods.
Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.
problem Distinguishing Lagrangian fillings of Legendrian submanifolds.
method Utilizes Newton polytopes associated with augmented values of Reeb chords.
result Newton polytopes can distinguish infinitely many distinct Lagrangian fillings.
Training neural networks under physical constraints using a stochastic augmented Lagrangian approachphysics.comp-ph
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
problem Offline constrained reinforcement learning with general function approximation.
method Primal-Dual-Critic Algorithm (PDCA) using a primal-dual approach.
result PDCA finds a near saddle point of the Lagrangian, nearly optimal for constrained RL.
The study explores Legendrian fillings and augmentations, providing methods to compute induced augmentations.
problem Understanding and computing Legendrian isotopy invariants through augmentations and fillings.
method Developed methods to compute induced augmentations based on Morse complex families and Legendrian cobordisms.
result Established methods to compute Legendrian isotopy invariants using augmentations and fillings.
Torsion found in knot homology, challenging augmentation theories.
problem Torsion in linearized contact homology for Legendrian knots.
method Examples of Legendrian knots with non-trivial homology over Z.
result Augmentations not induced by exact fillings, even mod 2.
A distributed semismooth Newton based augmented Lagrangian method for distributed optimizationmath.OC
A new method solves distributed optimization problems over networks.
problem Solving optimization problems over networks with local cost functions and limited communication.
method Distributed semismooth Newton based augmented Lagrangian method.
result The method efficiently solves distributed optimization problems over networks.
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
New augmentations of twist knots found that can't be filled.
problem Finding augmentations of twist knots that cannot be filled by orientable Lagrangian fillings.
method Using a Floer-theoretic version of a result from microlocal sheaf theory, showing augmentations cannot be induced by algebraic tori.
result Established new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings.
Efficiently solves Elastic Net in high dimensions with Newton method.
problem Feature selection in high-dimensional data with non-negligible collinearity.
method Semi-smooth Newton Augmented Lagrangian Method.
result Significantly reduces computational cost compared to competitors.
Visible Lagrangians in Hitchin systems are studied for pillowcase covers.
problem Visible Lagrangians in Hitchin systems intersecting non-trivially.
method Computation of Fourier-Mukai transforms and study of mirror dual branes.
result Mirror dual branes are closely related to Hausel's toy model.
Inexact and Stochastic Generalized Conditional Gradient with Augmented Lagrangian and Proximal Stepmath.OC
New algorithm tackles complex optimization problems with inexact and stochastic methods.
problem Solving complex optimization problems with inexact and stochastic methods.
method Developed ICGALP algorithm for composite minimization problems with inexact computations.
result Convergence of Lagrangian to an optimum and asymptotic feasibility of the affine constraint.
The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.
problem Understanding the relationship between Legendrian links and cluster theory.
method Using exact Lagrangian fillings and cluster theory, the paper establishes connections between Legendrian links and cluster varieties.
result The augmentation variety of certain Legendrian 2-bridge links is isomorphic to a product of cluster varieties.
New algorithm speeds up large-scale statistical inference.
problem Efficiently solving large-scale mean-field variational inference problems.
method Developed a novel primal-dual algorithm (PD-VI) and a block-preconditioned extension (PD-VI) for mean-field variational inference.
result PD-VI and PD-VI achieve faster convergence and better solution quality compared to existing methods.
A State-Augmented Approach for Learning Optimal Resource Management Decisions in Wireless Networkscs.LG
Optimizes wireless network resource management with state-augmented policies.
problem Optimizing network-wide utility with user performance constraints.
method State-augmented parameterization of RRM policy, using dual variables.
result Superior trade-off between mean, minimum, and 5th percentile rates.
Proposes TgNN-LD to improve neural network effectiveness and efficiency.
problem Limits in maintaining tradeoff between data and domain knowledge.
method Converts loss function to constrained form with PDEs, ECs, and EK as constraints, incorporating Lagrangian variables for equitable tradeoff.
result Improves prediction accuracy and conserves resources.
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczyński and the Parallel Coordinate Descent Method (PCDM) of Richtárik and Takáč. We show that …
New method fills cluster seeds with exact Lagrangian structures.
problem Surjectivity of map from Lagrangian fillings to cluster seeds.
method Construction of quiver with potential and Lagrangian disk surgeries.
result Trivial deformation space of quiver allows manipulation of fillings.
Affine hamiltonians are defined in the paper and their study is based especially on the fact that in the hyperregular case they are dual objects of lagrangians defined on affine bundles, by mean of natural Legendre maps. The variational problems for affine hamiltonians and lagrangians of order are studied, re…
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a …
We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R^3. This `homotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We prese…
We provide an explicit example of a non trivial Legendrian knot such that there exists a Lagrangian concordance from to where is the trivial Legendrian knot. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of to show that no Lagrangian co…
We investigate forms on supermanifolds defined as Lagrangians of ``copaths'' (that is, systems of equations, which may or may not specify submanifolds). For this, we consider direct products and study isomorphisms corresponding to simultaneously advancing the number of additional parameters …
The paper studies how Lagrangian cobordisms affect DGAs of Legendrian ends.
problem Understanding how Lagrangian cobordisms impact DGAs of Legendrian ends.
method Adapting the map induced by cobordisms on DGAs to linearizations using augmentations, and showing invariance under Lagrangian isotopy.
result The induced map on linearized Legendrian contact homology is invariant under Lagrangian isotopy under mild hypotheses.
We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra. This also impl…
Clean intersections of Lagrangian knots in 3D are impossible.
problem Prohibiting clean intersections of certain knots in 3D symplectic geometry.
method Symplectic field theory and algebraic constraints on augmentation varieties.
result No Hamiltonian diffeomorphism can cleanly intersect a specific type of knot's conormal bundle.
Paper proposes distributed optimization for federated learning with theoretical guarantees.
problem Privacy-preserving cross-organizational data collaboration in machine learning.
method Augmented Lagrangian technique for diverse communication topologies, termination criteria, and parameter update mechanisms.
result The proposed framework recovers classical optimization methods and provides strong performance in large-scale federated learning.
We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian cobordism on which all primitive of the Liouville form is not constant on the nega…
Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Functionmath.OC
A new decentralized algorithm DESTINY solves optimization over Stiefel manifold with single communication round.
problem Decentralized optimization over the Stiefel manifold with private data.
method Gradient tracking with approximate augmented Lagrangian function.
result DESTINY achieves global convergence with a single communication round.
Given the Lagrangian fibration and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the ``quantum'' corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration.
Unified DICE estimators as regularized Lagrangians for improved off-policy evaluation.
problem Improving off-policy evaluation from behavior-agnostic data.
method Unified derivation of DICE estimators as regularized Lagrangians of a linear program.
result Dual solutions offer greater flexibility and provide superior estimates in practice.
The Information Autoencoding Family: A Lagrangian Perspective on Latent Variable Generative Modelsstat.ML
A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately …
We introduce the notion of Kähler manifolds that are almost Einstein and we define a generalized mean curvature vector field along submanifolds in them. We prove that Lagrangian submanifolds remain Lagrangian, when deformed in direction of the generalized mean curvature vector field. For a Kähler manifold that is almos…
Paper proposes ASCCA for sparse CCA with trace Lasso regularization.
problem Sparse CCA in high-dimensional settings with correlated variables.
method Trace Lasso regularization, reformulated to Riemannian manifolds, inexact augmented Lagrangian method.
result Improved stability and interpretation of sparse CCA.