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We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
We present a new algorithm to train a robust neural network against adversarial attacks. Our algorithm is motivated by the following two ideas. First, although recent work has demonstrated that fusing randomness can improve the robustness…
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
Optimal Power Flow (OPF) is an important tool used to coordinate assets in electric power systems to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of…
We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set…
In low-voltage distribution networks, the integration of novel energy technologies can be accelerated through advanced optimization-based analytics such as network state estimation and network-constrained dispatch engines for distributed…
The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action…
Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer…
Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…
In real-time applications involving power flow equations, measuring of voltage phase angle difference of the connected buses is essential. However, it needs special techniques to measure voltage angle difference, which may enlarge the…
The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
Optimal power flow (OPF) is used to perform generation redispatch in power system real-time operations. N-1 OPF can ensure safe grid operations under diverse contingency scenarios. For large and intricate power networks with numerous…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier…