The past decade has seen the rapid growth of model based image reconstruction (MBIR)
algorithms, which are often applications or adaptations of convex optimization algorithms …

Mathematical optimization has always been at the heart of engineering, statistics, and
economics. In these applied domains, optimization concepts and methods have often been …

Backtracking line-search is an old yet powerful strategy for finding better step sizes to be
used in proximal gradient algorithms. The main principle is to locally find a simple convex …

We propose a new length formula that governs the iterates of the momentum method when
minimizing differentiable semialgebraic functions with locally Lipschitz gradients. It enables …

This paper proposes an inertial Bregman proximal gradient method for minimizing the sum
of two possibly nonconvex functions. This method includes two different inertial steps and …

By analyzing accelerated proximal gradient methods under a local quadratic growth
condition, we show that restarting these algorithms at any frequency gives a globally linearly …

In this paper, we consider a general inertial proximal gradient method with constant and
variable stepsizes for a class of nonconvex nonsmooth optimization problems. The …

Multiple measurement signals are commonly collected in practical applications, and joint
sparse optimization adopts the synchronous effect within multiple measurement signals to …

We propose a new family of inexact sequential quadratic approximation (SQA) methods,
which we call the inexact regularized proximal Newton (IRPN) method, for minimizing the …

For a symmetric positive semidefinite linear system of equations Q x= b Q x= b, where
x=(x_1, ..., x_s) x=(x 1,…, xs) is partitioned into s blocks, with s ≥ 2 s≥ 2, we show that each …