In 1963, Polyak proposed a simple condition that is sufficient to show a global linear
convergence rate for gradient descent. This condition is a special case of the Łojasiewicz …

We analyze the convergence rate of the alternating direction method of multipliers (ADMM)
for minimizing the sum of two or more nonsmooth convex separable functions subject to …

The block coordinate descent (BCD) method is widely used for minimizing a continuous
function f of several block variables. At each iteration of this method, a single block of …

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a
given set by a residual function, have proven to be extremely useful in analyzing the …

In this paper, we provide a unified iteration complexity analysis for a family of general block
coordinate descent methods, covering popular methods such as the block coordinate …

The sparse group Lasso is a widely used statistical model which encourages the sparsity
both on a group and within the group level. In this paper, we develop an efficient augmented …

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of
functions satisfying gradient dominance property with $1\le\alpha\le2 $ which holds in a …

Consider the problem of minimizing the sum of a smooth convex function and a separable
nonsmooth convex function subject to linear coupling constraints. Problems of this form arise …

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 …

Motivated by various applications in machine learning, the problem of minimizing a convex
smooth loss function with trace norm regularization has received much attention lately …