相关论文: Strengthening SONC Relaxations with Constraints De…

We briefly recall basics of the Moment-SOS hierarchy in polynomial optimization and the Christoffel-Darboux kernel (and the Christoffel function (CF)) in theory of approximation and orthogonal polynomials. We then (i) show a strong link…

In recent years, copositive programming has received significant attention for its ability to model hard problems in both discrete and continuous optimization. Several relaxations of copositive programs based on semidefinite programming…

We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust…

Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…

In this paper, we present an algorithm for synthesizing certificates---so-called barrier certificates---for safety of hybrid dynamical systems. Unlike the usual approach of using constraint solvers to compute the certificate from the system…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

We present a post-processing certification workflow for nonlinear elliptic boundary value problems that upgrades a standard finite element computation to a rigorous existence and output certificate. For a given approximate discrete state,…

We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that…

This paper investigates the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through an $\ell_0$ cardinality constraint. While branch-and-bound (BnB) frameworks can certify optimality…

Convex (specifically semidefinite) relaxation provides a powerful approach to constructing robust machine perception systems, enabling the recovery of certifiably globally optimal solutions of challenging estimation problems in many…

The robustness of deep neural networks (DNNs) against adversarial example attacks has raised wide attention. For smoothed classifiers, we propose the worst-case adversarial loss over input distributions as a robustness certificate. Compared…

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…

Signomials are obtained by generalizing polynomials to allow for arbitrary real exponents. This generalization offers great expressive power, but has historically sacrificed the organizing principle of ``degree'' that is central to…

In this work, the combine the theory of generalized critical values with the theory of iterated rings of bounded elements (real holomorphy rings). We consider the problem of computing the global infimum of a real polynomial in several…

We develop new list decoding algorithms for Tanner codes and distance-amplified codes based on bipartite spectral expanders. We show that proofs exhibiting lower bounds on the minimum distance of these codes can be used as certificates…

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by…

Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…

A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…

A polynomial that is a sum of squares (SOS) of other polynomials is evidently positive. The converse is not true, there are positive polynomials which are not SOS. This note focuses on the problem of certifying, in exact arithmetic, that a…

Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…