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To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

Computational Engineering, Finance, and Science · Computer Science 2024-02-23 Connor N. Mallon , Aaron W. Thornton , Matthew R. Hill , Santiago Badia

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Machine Learning · Statistics 2018-07-04 Luca Franceschi , Paolo Frasconi , Saverio Salzo , Riccardo Grazzi , Massimilano Pontil

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

Neural and Evolutionary Computing · Computer Science 2024-07-08 Ankur Sinha , Dhaval Pujara , Hemant Kumar Singh

We show how to extract alternative solutions for optimization problems solved by Benders Decomposition. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative…

Optimization and Control · Mathematics 2025-09-12 Matthew Viens , William E. Hart , Michael Ferris

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…

Machine Learning · Computer Science 2026-02-03 Jiancheng Tu , Wenqi Fan , Zhibin Wu

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

Machine Learning · Computer Science 2025-01-24 Jiannan Li , Yiyang Yang , Yao Wang , Shaojie Tang

Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…

Optimization and Control · Mathematics 2024-01-17 Artur M. Schweidtmann , Dominik Bongartz , Alexander Mitsos

Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming…

Optimization and Control · Mathematics 2019-10-29 J. N. Hooker

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-03-22 Dániel Berényi , András Leitereg , Gábor Lehel

Many annotation problems in computer vision can be phrased as integer linear programs (ILPs). The use of standard industrial solvers does not to exploit the underlying structure of such problems eg, the skeleton in pose estimation. The…

Computer Vision and Pattern Recognition · Computer Science 2017-09-14 Shaofei Wang , Konrad Kording , Julian Yarkony

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

Numerical Analysis · Mathematics 2023-10-11 Santiago Badia , Wei Li , Alberto F. Martín

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the…

Systems and Control · Computer Science 2016-11-18 Vito Cerone , Jean-Bernard Lasserre , Dario Piga , Diego Regruto

We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…

Optimization and Control · Mathematics 2026-04-09 Pierre Bonami , Sanjeeb Dash , Anton Derkach , Andrea Lodi

This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization problem, in which both distributed agents and a central coordinator contribute independent, potentially conflicting…

Optimization and Control · Mathematics 2025-07-21 Roberto Morales , Umberto Biccari

This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…

Optimization and Control · Mathematics 2020-07-28 Wei Wei

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

Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…

Information Theory · Computer Science 2020-10-16 Mengyuan Lee , Ning Ma , Guanding Yu , Huaiyu Dai

Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…

Optimization and Control · Mathematics 2025-04-14 Federico Parolin , Yu Weng , Paolo Colbertaldo , Ruaridh Macdonald