Reliable and efficient trajectory generation methods are a fundamental need for
autonomous dynamical systems. The goal of this article is to provide a comprehensive …

Recently, alternating direction method of multipliers (ADMM) attracts much attentions from
various fields and there are many variant versions tailored for different models. Moreover, its …

Many tasks in machine learning and signal processing can be solved by minimizing a
convex function of a measure. This includes sparse spikes deconvolution or training a …

In this paper, we study the implicit regularization of the gradient descent algorithm in
homogeneous neural networks, including fully-connected and convolutional neural …

Gradient Descent Only Converges to Minimizers Page 1 JMLR: Workshop and Conference
Proceedings vol 49:1–12, 2016 Gradient Descent Only Converges to Minimizers Jason D. Lee …

We establish that first-order methods avoid strict saddle points for almost all initializations.
Our results apply to a wide variety of first-order methods, including (manifold) gradient …

We study the implicit regularization imposed by gradient descent for learning multi-layer
homogeneous functions including feed-forward fully connected and convolutional deep …

This paper shows that error bounds can be used as effective tools for deriving complexity
results for first-order descent methods in convex minimization. In a first stage, this objective …

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract
convergence result for descent methods satisfying a sufficient-decrease assumption, and …

We study the convergence properties of an alternating proximal minimization algorithm for
nonconvex structured functions of the type: L (x, y)= f (x)+ Q (x, y)+ g (y), where f and g are …