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Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Autonomous robots are widely utilized for mapping and exploration tasks due to their cost-effectiveness. Multi-robot systems offer scalability and efficiency, especially in terms of the number of robots deployed in more complex…
Machine learning interatomic potentials (MLIPs) provide a computationally efficient alternative to quantum mechanical simulations for predicting material properties. Message-passing graph neural networks, commonly used in these MLIPs, rely…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it…
Autonomous driving at intersections is one of the most complicated and accident-prone traffic scenarios, especially with mixed traffic participants such as vehicles, bicycles and pedestrians. The driving policy should make safe decisions to…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
In this paper we consider the problem of coordinating autonomous vehicles approaching an intersection. We cast the problem in the distributed optimisation framework and propose an algorithm to solve it in real time. We extend previous work…
In highly interactive driving scenarios, the actions of one agent greatly influences those of its neighbors. Planning safe motions for autonomous vehicles in such interactive environments, therefore, requires reasoning about the impact of…
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution…
The use of machine learning in the self-driving industry has boosted a number of recent advancements. In particular, the usage of large deep learning models in the perception and prediction stack have proved quite successful, but there…
Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety…
We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…