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Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…

This paper investigates the distributed stochastic nonconvex and nonsmooth composite optimization problem. Existing stochastic typically rely on uniform step size strictly bounded by global network parameters, such as the maximum node…

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…

In this paper, we develop unrolled neural networks to solve constrained optimization problems, offering accelerated, learnable counterparts to dual ascent (DA) algorithms. Our framework, termed constrained dual unrolling (CDU), comprises…

Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model…

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired…

This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…

In this paper, we study a class of non-convex optimization problems known as multi-affine quadratic equality constrained problems, which appear in various applications--from generating feasible force trajectories in robotic locomotion and…

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…

In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…

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…

In accelerated MRI reconstruction, the anatomy of a patient is recovered from a set of under-sampled and noisy measurements. Deep learning approaches have been proven to be successful in solving this ill-posed inverse problem and are…

We consider a class of structured, nonconvex, nonsmooth optimization problems under orthogonality constraints, where the objectives combine a smooth function, a nonsmooth concave function, and a nonsmooth weakly convex function. This class…

The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. For this problem class, conventional optimizers suffer from small step sizes…

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…

In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this…

Learning to learn has emerged as an important direction for achieving artificial intelligence. Two of the primary barriers to its adoption are an inability to scale to larger problems and a limited ability to generalize to new tasks. We…