arXiv subjects

Alexander J Gallo

Publications and source records attributed to Alexander J Gallo.

2 recordsLinked to original sources

arXiv2026

Robustness certificates in data-driven non-convex optimization with additively-uncertain constraints

We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite data-set, according to the scenario robust optimization paradigm. By exploiting the structure of the constraints, we show that both a priori and a posteriori distribution-free probabilistic robustness certificates for a possibly sub-optimal solution to the resulting data-driven optimization problem can be obtained with minimal computational effort. Building on these results, we also discuss a one-shot and an incremental procedure to determine the size of the data-set so as to guarantee a user-chosen robustness level. Notably, both the a posteriori robustness assessment and incremental data-set sizing do not require to solve the non-convex scenario program. A comparative analysis performed on the unit commitment problem using real data reveals a limited increase in conservativeness with a significant computational saving with respect to the application of scenario theory results for general, non necessarily structured, non-convex problems.

math.OC↗

arXiv2025

Security of Gradient Tracking Algorithms Against Malicious Agents

Consensus algorithms are fundamental to multi-agent distributed optimization, and their security under adversarial conditions is an active area of research. While prior works primarily establish conditions for successful global consensus under attack, little is known about system behavior when these conditions are violated. This paper addresses this gap by investigating the robustness of the Wang--Elia algorithm, which is a robust to noise version of gradient tracking algorithm, in the presence of malicious agents. We consider a network of agents collaboratively minimizing a global cost function, where a subset of agents may transmit faulty information to disrupt consensus. To quantify resilience, we formulate a security metric as an optimization problem, which is rooted in centralized attack detection literature. We provide a tractable reformulation of the optimization problem, and derive conditions under which the metric becomes unbounded, identifying undetectable attack signals that reveal inherent vulnerabilities. To facilitate design and analysis, we propose a well-posed variant of the metric and propose design methods to enhance network robustness against stealthy adversarial attacks. Numerical examples demonstrate the effectiveness of the proposed framework to enhance the resilience of multi-agent distributed optimization.

eess.SY↗