arXiv research

Develops an accelerated algorithm for solving nonmonotone generalized equations.

Large stepsizes can accelerate gradient descent for logistic regression.

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves…

Data coarse graining improves model performance by filtering out less relevant features.

A new L-BFGS method tackles large-scale optimization with fewer evaluations.

In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming pro…

The paper explores arbitrage opportunities in derivative markets under specific conditions.

We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize $1/L$ satisfies the $L…

New method solves root-finding problems with faster convergence.

This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.

We consider the problem of minimizing a difference-of-convex (DC) function, which can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous possibly nonsmooth concave function. We refine the convergence analysis in [38] for the proximal DC algorithm …

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing regularizer. In this paper, motivated by the success of extrapolation techniques in accele…

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing spars…

Develops variance-reduced methods for solving generalized equations.

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components (PCs) are usually linear combinations of all the original variables, and it is thus…

The paper studies how more data affects prediction risk in high-dimensional models.

New variance-reduction methods solve stochastic composite inclusions.

Improves CNN stability by translating classical signal denoising methods.

We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the mo…

In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting…

In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the origin…

New algorithms solve stochastic variational inequalities without bounded variance assumption.

Analysis of ridge regression under concept shift reveals nontrivial effects on generalization performance.

UBI model proves financial equilibrium exists.

Improved variational inequality algorithms using adaptive step sizes.

Synthetic data augmentation can improve imbalanced classification metrics.

FACMAC combines deep policy gradients with factored critic for multi-agent reinforcement learning.

This paper extends financial theory to measure learnable market structure under computational constraints.

The study uses Random Matrix Theory to identify structural changes in stock markets during shocks.

We simplify neural networks to 3D to study their topological changes.

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear …

Proves weak convergence equals mean convergence in GGC.

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic notions which have been applied to study sequences of submanifolds in Euclidean…

The abstract discusses convergence properties of Lipschitz functions and sets defined by equations.

Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.

Studied SGD convergence under weak conditions.

Study on convergence rate of $Q$-curvature flow in 6 dimensions.

The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce …

Establishes geometric convergence of iterative optimization algorithms.

Uniform counting formulas for orthogeodesics in Kleinian groups converge.

The paper explores null distance convergence for warped product spacetimes.

New quasi-Newton method guarantees global superlinear convergence.

We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.

The article introduces a new convergence concept for Lorentzian spaces and applies it to generalized cones.

AdaBoost's classifier and margins converge to a known value.

Study shows gap between uniform convergence and test error in random feature models.

The Sinkhorn-Knopp derivatives converge with linear rate.

The paper examines convergence of distances in Lipschitz structures on manifolds.