Related papers: Verifying Integer Programming Results
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…
Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Automatic software verification tools help to find hard-to-detect faults in programs checked against specified requirements non-interactively. Besides, they can prove program correctness formally under certain assumptions. These…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
The proliferation of machine learning-based methods for Mixed-Integer Linear Programming (MILP) instance generation has surged, driven by the need for diverse training datasets. However, a critical question remains: Are these generated…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
The article presents and evaluates a scalable algorithm for validating solutions of linear programming problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce solvable tuple patterns (STPs) and conjunctive STPs…
Following the recent push for trustworthy AI, there has been an increasing interest in developing contrastive explanation techniques for optimisation, especially concerning the solution of specific decision-making processes formalised as…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. Unfortunately, dual certificates may not exist under…
Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
We develop a real-time feasible mixed-integer programming-based decision making (MIP-DM) system for automated driving. Using a linear vehicle model in a road-aligned coordinate frame, the lane change constraints, collision avoidance and…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer…
Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…