Related papers: WANCO: Weak Adversarial Networks for Constrained O…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve…
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…
Deep Neural Networks (DNNs) have recently achieved great success in many classification tasks. Unfortunately, they are vulnerable to adversarial attacks that generate adversarial examples with a small perturbation to fool DNN models,…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional…
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…
In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the…
With the increasing amount of available data and advances in computing capabilities, deep neural networks (DNNs) have been successfully employed to solve challenging tasks in various areas, including healthcare, climate, and finance.…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
Adversarial attack algorithms are dominated by penalty methods, which are slow in practice, or more efficient distance-customized methods, which are heavily tailored to the properties of the distance considered. We propose a white-box…
Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…
Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…