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We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other nonsmooth. The key highlight is a natural property of the resulting problem's structure that yields a…
We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing…
We tackle highly nonconvex, nonsmooth composite optimization problems whose objectives comprise a Moreau-Yosida regularized term. Classical nonconvex proximal splitting algorithms, such as nonconvex ADMM, suffer from lack of convergence for…
The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
Deep neural network learning can be formulated as a non-convex optimization problem. Existing optimization algorithms, e.g., Adam, can learn the models fast, but may get stuck in local optima easily. In this paper, we introduce a novel…
The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…
In this work, we solve a 49-year open problem, the general optimal step-size for ADMM-type algorithms. For a convex program: $\text{min.} \,\, f({x}) + g({z})$, $\text{s.t.}\, {A}{x} - {B}{z} = {c} $, given an arbitrary fixed-point…
Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
Despite their tremendous successes, convolutional neural networks (CNNs) incur high computational/storage costs and are vulnerable to adversarial perturbations. Recent works on robust model compression address these challenges by combining…
In this paper, we consider a novel optimization design for multi-waveguide pinching-antenna systems, aiming to maximize the weighted sum rate (WSR) by jointly optimizing beamforming coefficients and antenna position. To handle the…