We propose machine learning-based (ML) methods to accelerate convergence to global
solutions for the AC Optimal Power Flow (AC-OPF) problem. In particular, for the non-convex …

In this paper, we propose a novel Semidefinite Programming (SDP) relaxation of the Optimal
Power Flow (OPF) problem. The proposed formulation utilizes the Line-Wise Model (LWM) …

Power flow refers to the injection of power on the lines of an electrical grid, so that all the
injections at the nodes form a consistent flow within the network. Optimality, in this setting, is …

In recent years, there has been significant interest in the development of machine learning-
based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant …

This paper focuses on designing edge-weighted networks, whose robustness is
characterized by maximizing Algebraic connectivity, or the second smallest eigenvalue of …

We present the results of a comprehensive bench-marking effort aimed at evaluating and
comparing state-of-the-art open-source tools for solving the Alternating-Current Optimal …

Distribution network constrained mathematical optimization is key technology to enable
advanced distribution network management. In recent years, a growing amount of articles on …

We report the experimental results on certifying 1% global optimality of solutions of AC-OPF
instances from PGLiB via the CS-TSSOS hierarchy—a moment-SOS based hierarchy that …

Mathematical models representing the behavior of electrical loads are an important part of
any optimal power flow problem. The current state-of-the-art in unbalanced optimal power …

This thesis deals with approximating sets using Lasserre's moment-SOS hierarchy. The
motivation is the increasing need for efficient methods to approximate sets of secure …