Related papers: A Unifying Complexity-Certification Framework for …
For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the…
We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which is an extension of the well known Boolean Quadratic Programming Problem (BQP). Applications of the BBQP include mining discrete patterns from binary data,…
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…
Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…
We present a solver for Mixed Integer Programs (MIP) developed for the MIP competition 2022. Given the 10 minutes bound on the computational time established by the rules of the competition, our method focuses on finding a feasible solution…
Planning in hybrid systems with both discrete and continuous control variables is important for dealing with real-world applications such as extra-planetary exploration and multi-vehicle transportation systems. Meanwhile, generating…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…
We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer…
In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications.…
Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have…
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…
The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end,…
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…