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Jeroslow and Lowe gave an exact geometric characterization of subsets of $\mathbb{R}^n$ that are projections of mixed-integer linear sets, also known as MILP-representable or MILP-R sets. We give an alternate algebraic characterization by…
In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…
We address the Interval Data Min-Max Regret 0-1 Integer Linear Programming problem (MMR-ILP), a variant of the 0-1 Integer Linear Programming problem where the objective function coefficients are uncertain. We solve MMR-ILP using a…
We study the AutoML problem of automatically configuring machine learning pipelines by jointly selecting algorithms and their appropriate hyper-parameters for all steps in supervised learning pipelines. This black-box (gradient-free)…
The efficient allocation of human resources is a critical concern in software development and other industries. This paper introduces a rigorous mathematical methodology for task assignment, employing Mixed Integer Linear Programming (MILP)…
Designing reliable integrated energy systems for industrial processes requires optimization and verification models across multiple fidelities, from architecture-level sizing to high-fidelity dynamic operation. However, model mismatch…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…
First-principles atomistic simulations are essential for understanding complex material phenomena but are fundamentally limited by their computational cost. While Machine Learning Interatomic Potentials (MLIPs) have drastically improved…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
In many operational contexts, solutions to NP-hard combinatorial optimization problems, modeled by means of Mixed-Integer Linear Programming (MILP), may become infeasible due to unpredictable disruptions. Typically, reoptimizing by solving…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
As a result of the ever increasing complexity of configuring and fine-tuning machine learning models, the field of automated machine learning (AutoML) has emerged over the past decade. However, software implementations like Auto-WEKA and…
As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a…
Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via…
In this work, we explore the efficacy of rectified linear unit artificial neural networks in addressing the intricate challenges of convoluted constraints arising from feedback linearization mapping. Our approach involves a comprehensive…
We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…