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Meeting minimum data rate constraints is a significant challenge in wireless communication systems, particularly as network complexity grows. Traditional deep learning approaches often address these constraints by incorporating penalty…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
Enabling low precision implementations of deep learning models, without considerable performance degradation, is necessary in resource and latency constrained settings. Moreover, exploiting the differences in sensitivity to quantization…
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…
Lifted neural networks (i.e. neural architectures explicitly optimizing over respective network potentials to determine the neural activities) can be combined with a type of adversarial training to gain robustness for internal as well as…
In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle…
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…
Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must…
State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against it. Formulated as a min-max problem, it…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data…
This research presents a novel method using an adversarial neural network to solve the eigenvalue topology optimization problems. The study focuses on optimizing the first eigenvalues of second-order elliptic and fourth-order biharmonic…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…