The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in expectation. In this paper, we establish various generalization error bounds...

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange with some neighbors, although its cost function possibly depends on strategies of all agents. The few existing methods build projected pseudo-gradient dynamics, and require either double-layer iterations or conservative conditions step sizes. To overcome bot...

Purpose: To describe a case series of young adult patients with isolated chronic proximal biceps tendinitis refractory to conservative care found to have anatomic long head biceps tendon (LHBT) origin variations who underwent arthroscopic-assisted subpectoral biceps tenodesis. Methods: Patients were included in this retrospective case series if they met all the following criteria: 1) had ...

The main shortcoming of sparse recovery with a convex regularizer is that it is a biased estimator and therefore will result in a suboptimal performance in many cases. Recent studies have shown, both theoretically and empirically, that non-convex regularizer is able to overcome the biased estimation problem. Although multiple algorithms have been developed for sparse recovery with non-convex re...

In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle problem choose continuous forward-backward approach and introduce dynamical system which is formulated means partial gradients function proximal point operator functions. Moreover, consider variable rates implicity resulting syste...

We consider proximal gradient methods for minimizing a composite function of differentiable and convex function. To accelerate the general methods, we focus on quasi-Newton type based mappings scaled by matrices. Although it is usually difficult to compute mappings, applying memoryless symmetric rank-one (SR1) formula makes this easier. Since (quasi-Newton) matrices must be positive definite, d...

This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and (nonseparable) nonsmooth function, both which are allowed to be nonconvex. The main tool in our analysis is forward-backward envelope, serves as particularly suitable continuous real-valued Lyapunov function. Global linear convergence results established when cost satisfies K...

In this paper, we study the low-rank matrix minimization problem, where loss function is convex but nonsmooth and penalty term defined by cardinality function. We first introduce an exact continuous relaxation, that is, both problems have same minimizers optimal value. particular, a class of lifted stationary points relaxed problem show any local minimizer must be point. addition, derive lower ...

A class of `1-regularized optimization problems with orthogonality constraints has been used to model various applications arising from physics and information sciences, e.g., compressed modes for variational problems. Such optimization problems are difficult to solve due to the non-smooth objective function and nonconvex constraints. Existing methods either are not applicable to such problems,...

We address the problem of planning collision-free paths for multiple agents using optimization methods known as proximal algorithms. Recently this approach was explored in Bento et al. (2013), which demonstrated its ease of parallelization and decentralization, the speed with which the algorithms generate good quality solutions, and its ability to incorporate different proximal operators, each ...