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Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed…
Training of neural networks amounts to nonconvex optimization problems that are typically solved by using backpropagation and (variants of) stochastic gradient descent. In this work we propose an alternative approach by viewing the training…
The widespread deployment of inverter-based resources (IBRs) renders distribution systems susceptible to transmission-level faults. This paper presents a comprehensive analysis of the impact of transmission-level faults on 3-phase and…
Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting…
In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by…
Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using…
This paper addresses the multivariable gradient-based extremum seeking control (ESC) subject to saturation. Two distinct saturation scenarios are investigated here: saturation acting on the input of the function to be optimized, which is…
This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks, consisting of multiple interacting networks. However, despite significant research in…
Interference mitigation techniques are essential for improving the performance of interference limited wireless networks. In this paper, we introduce novel interference mitigation schemes for wireless cellular networks with space division…
Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal…
Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free linear quadratic regulator (LQR), and linear feedforward…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
The communication of gradients is a key bottleneck in distributed training of large scale machine learning models. In order to reduce the communication cost, gradient compression (e.g., sparsification and quantization) and error…
Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…