arXiv research

A new method tackles nonconvex optimization with penalties and proximal terms.

Paper proposes distributed optimization for federated learning with theoretical guarantees.

New methods for convex optimization with locally Lipschitz gradient, achieving faster convergence.

A new method solves distributed optimization problems over networks.

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…

Improves robustness of high-dimensional regression with rank objective and group lasso regularization.

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the …

Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an $ε$ stationary point where the expected norm of the subgradient of corresponding augmented Lag…

Paper tackles multivariate shape-constrained convex regression problems.

Paper solves optimization problems with convex expectation constraints using a new algorithm.

New algorithm tackles complex optimization problems with inexact and stochastic methods.

A new algorithm solves the metric nearness problem efficiently.

A new method solves complex constrained minimax problems.

Unified Lagrangian-based methods for nonsmooth nonconvex optimization.

Paper proposes a new method to find approximate SOSP for nonconvex constrained optimization problems.

For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-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 $\mathcal{A}_{\infty}$ 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…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…

Study of Legendrian links using Floer theory and cluster varieties.

Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.

Stochastic approach improves neural network training for kinetic simulations.

The study explores Legendrian fillings and augmentations, providing methods to compute induced augmentations.

Torsion found in knot homology, challenging augmentation theories.

New method solves constrained optimization problems efficiently.

New augmentations of twist knots found that can't be filled.

Efficiently solves Elastic Net in high dimensions with Newton method.

The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.

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 …

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmented Lagrangian b…

New method fills cluster seeds with exact Lagrangian structures.

Develops consistent approximations for composite optimization problems.

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 $Λ$ such that there exists a Lagrangian concordance from $Λ_0$ to $Λ$ where $Λ_0$ is the trivial Legendrian knot. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of $Λ$ to show that no Lagrangian co…

The paper studies how Lagrangian cobordisms affect DGAs of Legendrian ends.

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods. This paper proposes two accelerated methods towards solving structured linearly co…

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…

New algorithm reduces regret in CMDPs without cancellation of errors.

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.

SMP model preserves proximity and permutation in graph neural networks.

Augment small datasets with synthetic backgrounds to train lightweight CNNs for human pose estimation.

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…

A new decentralized algorithm DESTINY solves optimization over Stiefel manifold with single communication round.

Paper proposes ASCCA for sparse CCA with trace Lasso regularization.

The paper develops methods for time-varying constrained online convex optimization.

New offline RL algorithms tackle partial data coverage with optimal performance and practicality.

Method solves nonconvex constrained optimization problems with a new augmented Lagrangian approach.