Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.14004

Distributed Convex Second-Order Optimization for AC/DC Hybrid Distribution Systems within PROcess Orchestration Framework

Xinliang Dai·Yuning Jiang·Junyi Zhai·Jianlei Liu·Thorsten Schlachter·Colin N. Jones·Xiao-Ping Zhang·Veit Hagenmeyer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Existing operation formulations for AC/DC distribution grid often oversimplify the interplay of AC/DC interconnections and VSC characteristics. Moreover, current distributed algorithms depend on gradient-based methods, which achieve only linear convergence rates and struggle to scale efficiently for large systems. This paper proposes a convex ALADIN variant that exploits second-order derivatives of convex subproblems, achieving locally quadratic convergence for distributed nonlinear but convex optimization problems. Then, this convex ALADIN is applied to a separable AC/DC OPF model for AC/DC hybrid distribution grid, explicitly incorporating complicated AC/DC interconnections and multiple droop-controlled VSCs while retaining computational traceability. To bridge theory with practice, we implement the distributed convex second-order optimization framework using the PROcess Orchestration Framework, a co-simulation platform that automates workflow design, model integration, and distributed execution via a user-friendly graphical interface, eliminating manual coding. Numerical results illustrate effectiveness of the proposed model.

Explore related subjects

math.OCcs.SYeess.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xinliang Dai, Yuning Jiang, Junyi Zhai, Jianlei Liu, Thorsten Schlachter, Colin N. Jones, Xiao-Ping Zhang, Veit Hagenmeyer. 2026-09-12. Distributed Convex Second-Order Optimization for AC/DC Hybrid Distribution Systems within PROcess Orchestration Framework. https://doi.org/10.1109/tpwrs.2026.3658172

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

We address the behavior of idealized deep residual neural networks (ResNets), modeled via an optimal control problem set over continuity (or adjoint transport) equations. The continuity equations describe the statistical evolution of the features in the asymptotic regime where the layers of the network form a continuum. The velocity field is expressed through the network activation function, which is itself viewed as a function of the statistical distribution of the network parameters (weights and biases). From a mathematical standpoint, the control is interpreted in a relaxed sense, taking values in the space of probability measures over the set of parameters. We investigate the optimal behavior of the network when the cost functional arises from a regression problem and includes an additional entropic regularization term on the distribution of the parameters. In this framework, we focus in particular on the existence of stable optimizers --that is, optimizers at which the Hessian of the cost is non-degenerate. We show that, for an open and dense set of initial data, understood here as probability distributions over features and associated labels, there exists a unique stable global minimizer of the control problem. Moreover, we show that such minimizers satisfy a local Polyak--Lojasiewicz inequality, which can lead to exponential convergence of the corresponding gradient descent when the initialization lies sufficiently close to the optimal parameters. This result thus demonstrates the genericity (with respect to the distribution of features and labels) of the Polyak--Lojasiewicz condition in ResNets with a continuum of layers and under entropic penalization.

math.OC↗
arXiv2026

A regret minimization approach to fixed-point iterations

We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical Krasnoselskii--Mann iterations, as the latter are recovered by converting the Online Gradient Descent algorithm. This approach yields new simple iterations for finding fixed points of non-self operators. We also focus on converting algorithms from the AdaGrad family of regret minimizers, and thus obtain fixed point iterations with adaptive guarantees of a new kind. Numerical experiments on various problems demonstrate faster convergence of AdaGrad-based fixed point iterations over Krasnoselskii--Mann iterations.

math.OC↗
arXiv2026

Variational Analysis in Spectral Decomposition Systems

This work is concerned with the variational analysis of functions defined on Euclidean spaces whose values depend solely on certain invariants (``spectrum'') of their arguments, a class we term ``spectral functions.'' Building on our previous work \cite{PartI} on the convex analysis of such functions, we work in the abstract framework of spectral decomposition systems, which covers a wide range of previously studied settings, including eigenvalue decomposition of Hermitian matrices and singular value decomposition of rectangular matrices, and allows the derivation of new results in more general settings such as normal decomposition systems. The main results of this work provide constructive formulae for computing the regular, limiting, and Clarke subdifferentials of a spectral function in terms of the corresponding objects of the associated invariant function. Finally, we obtain a generalization of Lidski\uı's theorem on the spectrum of additive perturbations of Hermitian matrices to arbitrary spectral decomposition systems.

math.OC↗