Related papers: Certified Constraint Propagation and Dual Proof An…

This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. To implement the dual variable update, we create a new prox function for nonnegative measures which turns…

In this paper we show how prescritive type checking and constraint solving can be combined to increase automation during software verification. We do so by defining a type system and implementing a typechecker for {log} (read `setlog'), a…

In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through…

For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semidefinite programming (SDP) relaxation…

We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by extension to decrease energy consumption during the solve. The lower the precision…

Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…

Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…

Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…

We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning…

When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at…

This work studies constrained blackbox optimization problems that cannot be solved in reasonable time due to prohibitive computational costs. This challenge is especially prevalent in industrial applications, where blackbox evaluations are…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is…

Neural networks are part of many contemporary NLP systems, yet their empirical successes come at the price of vulnerability to adversarial attacks. Previous work has used adversarial training and data augmentation to partially mitigate such…

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…

We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be…

State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…

Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there may exist large, meaningful perturbations that do not…

Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…