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.

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 …

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…

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

Paper tackles multivariate shape-constrained convex regression problems.

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

Unified Lagrangian-based methods for nonsmooth nonconvex optimization.

A new method solves complex constrained minimax problems.

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

A new algorithm solves the metric nearness problem efficiently.

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

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,…

New method solves constrained optimization problems efficiently.

Efficiently solves Elastic Net in high dimensions with Newton method.

Stochastic approach improves neural network training for kinetic simulations.

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

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…

Develops consistent approximations for composite 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…

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…

Study of Legendrian links using Floer theory and cluster varieties.

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

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 method fills cluster seeds with exact Lagrangian structures.

Torsion found in knot homology, challenging augmentation theories.

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

New algorithm reduces regret in CMDPs without cancellation of errors.

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

In this paper, we propose a novel approach in order to recover a quantized matrix with missing information. We propose a regularized convex cost function composed of a log-likelihood term and a Trace norm term. The Bi-factorization approach and the Augmented Lagrangian Method (ALM) are applied to find the global minimi…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem …

A new method solves large-scale sparse group square-root Lasso problems efficiently.

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

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…

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

Paper proposes ASCCA for sparse CCA with trace Lasso regularization.

Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…

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

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

The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical fast convergence rate under weak conditions. However, for problems such as X-ray co…

New algorithm solves stochastic optimization problems with unknown gradients.