The importance of the step size in stochastic optimization has been confirmed both
theoretically and empirically during the past few decades and reconsidered in recent years …

We propose a family of spectral gradient methods, whose stepsize is determined by a
convex combination of the long Barzilai–Borwein (BB) stepsize and the short BB stepsize …

We propose a new stepsize for the gradient method. It is shown that this new stepsize will
converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's …

The non-Lipschitz piecewise constant Mumford–Shah model has been shown effective for
image labeling and segmentation problems, where the non-Lipschitz isotropic ℓ p (0< p< 1) …

Stochastic variance reduced gradient (SVRG) methods are important approaches to
minimize the average of a large number of cost functions frequently arising in machine …

This paper studies optimization problems over multi-agent systems, in which all agents
cooperatively minimize a global objective function expressed as a sum of local cost …

We consider the problem of minimizing the sum of an average of a large number of smooth
convex component functions and a possibly nonsmooth convex function that admits a simple …

We consider the asymptotic behavior of a family of gradient methods, which include the
steepest descent and minimal gradient methods as special instances. It is proved that each …

Nonmonotone gradient methods generally perform better than their monotone counterparts
especially on unconstrained quadratic optimization. However, the known convergence rate …

Solution of sparse linear complementarity problem (LCP) has been widely discussed in
many applications. In this paper, we consider the ℓ p regularization problem with …