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Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull.…

Discrete Mathematics · Computer Science 2020-11-13 Matthias Walter

Although large language models (LLMs) have achieved revolutionary breakthroughs in many fields, their large model size and high computational cost pose significant challenges for practical deployment on resource-constrained edge devices. To…

Machine Learning · Computer Science 2025-10-29 Yao Lu , Yuqi Li , Wenbin Xie , Shanqing Yu , Qi Xuan , Zhaowei Zhu , Shiping Wen

Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the disjunctive proofs of optimality from prior solves to…

Optimization and Control · Mathematics 2025-11-21 Shannon Kelley , Aleksandr M. Kazachkov , Ted Ralphs

We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…

Optimization and Control · Mathematics 2018-07-03 Dajun Yue , Jiyao Gao , Bo Zeng , Fengqi You

We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Ján Boldocký , Shahriar Dadras Javan , Martin Gulan , Martin Mönnigmann , Ján Drgoňa

Cutting-plane methods are well-studied localization(and optimization) algorithms. We show that they provide a natural framework to perform machinelearning ---and not just to solve optimization problems posed by machinelearning--- in…

Machine Learning · Computer Science 2015-08-13 Liva Ralaivola , Ugo Louche

Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and…

Optimization and Control · Mathematics 2024-12-11 Xuefeng Zhang , Liangyu Chen , Zhengfeng Yang , Zhenbing Zeng

We present a computationally tractable framework for real-time predictive control of multi-chiller plants that involve both discrete and continuous control decisions coupled through nonlinear dynamics, resulting in a mixed-integer optimal…

Systems and Control · Electrical Eng. & Systems 2026-03-31 Ján Boldocký , Cary Faulkner , Elad Michael , Martin Gulan , Aaron Tuor , Ján Drgoňa

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to…

Optimization and Control · Mathematics 2018-05-09 Santanu S. Dey , Marco Molinaro

Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…

Optimization and Control · Mathematics 2025-11-04 Hòa T. Bùi , Alberto De Marchi

We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the…

Optimization and Control · Mathematics 2020-08-27 Kennedy Araujo , Tiberius Bonates , Bruno Prata

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

Optimization and Control · Mathematics 2023-11-17 Daniel Porumbel

We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training…

Machine Learning · Computer Science 2018-10-01 SueYeon Chung , Uri Cohen , Haim Sompolinsky , Daniel D. Lee

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…

Optimization and Control · Mathematics 2021-03-04 Dimitris Bertsimas , Michael Lingzhi Li

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…

Optimization and Control · Mathematics 2018-02-09 Bin Yu , John E. Mitchell , Jong-Shi Pang

A conflict graph represents logical relations between binary variables, and effective use of the graph can significantly accelerate branch-and-cut solvers for mixed-integer programming (MIP). In this paper we develop efficient parallel…

Optimization and Control · Mathematics 2025-06-18 Yongzheng Dai , Chen Chen

This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…

Discrete Mathematics · Computer Science 2024-10-14 Pierre Fouilhoux , Lucas Létocart , Yue Zhang

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

Quantum Physics · Physics 2025-10-16 Matteo Vandelli , Francesco Ferrari , Daniele Dragoni

We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…

Computer Vision and Pattern Recognition · Computer Science 2019-08-05 Margret Keuper , Jovita Lukasik , Maneesh Singh , Julian Yarkony

We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…

Optimization and Control · Mathematics 2024-05-07 Akul Bansal , Simge Küçükyavuz