Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

Conic optimization has recently emerged as a powerful tool for designing tractable and
guaranteed algorithms for power system operation. On the one hand, tractability is crucial …

Despite their impressive performance on diverse tasks, neural networks fail catastrophically
in the presence of adversarial inputs—imperceptibly but adversarially perturbed versions of …

The power flow equations relate the power injections and voltages in an electric power
system and are therefore key to many power system optimization and control problems …

We consider the problem of generating motion plans for a robot that are guaranteed to
succeed despite uncertainty in the environment, parametric model uncertainty, and …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

In a recent article, we have shown how to learn controllers for unknown linear systems using
finite-length noisy data by solving linear matrix inequalities. In this article, we extend this …

This paper is concerned with polynomial optimization problems. We show how to exploit
term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of …

This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-
scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously …

We investigate the addition of constraints on the function image and its derivatives for the
incorporation of prior knowledge in symbolic regression. The approach is called shape …