Related papers: Dual Lagrangian Learning for Conic Optimization

There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…

Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with…

We propose Deep Companion Learning (DCL), a novel training method for Deep Neural Networks (DNNs) that enhances generalization by penalizing inconsistent model predictions compared to its historical performance. To achieve this, we train a…

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…

A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial differential equations. The solver consists of a deep neural…

Using deep neural networks to predict the solutions of AC optimal power flow (ACOPF) problems has been an active direction of research. However, because the ACOPF is nonconvex, it is difficult to construct a good data set that contains…

As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…

Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…

This correspondence considers the resource allocation problem in wireless interference channel (IC) under link outage constraints. Since the optimization problem is non-convex in nature, existing approaches to find the optimal power…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline, i.e., training, pruning and retraining (fine-tuning) significantly increases the…

The linear coefficient in a partially linear model with confounding variables can be estimated using double machine learning (DML). However, this DML estimator has a two-stage least squares (TSLS) interpretation and may produce overly wide…

Advancements in deep learning are revolutionizing science and engineering. The immense success of deep learning is largely due to its ability to extract essential high-dimensional (HD) features from input data and make inference decisions…

This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly…