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In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
Mutual localization is essential for coordination and cooperation in multi-robot systems. Previous works have tackled this problem by assuming available correspondences between measurements and received odometry estimations, which are…
The size and complexity of modern astronomical surveys has grown to the point where, in many cases, traditional human scheduling of observations are tedious at best and impractical at worst. Automated scheduling algorithms present an…
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…
This paper proposes a global optimization method for it ensures finding good solutions while solving the unit commitment (UC) problem with carbon emission trading (CET). This method con-sists of two parts. In the first part, a sequence of…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
We compute $\epsilon$-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is…
Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is…
Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor…
Many of the classic graph problems cannot be solved in the Massively Parallel Computation setting (MPC) with strongly sublinear space per machine and $o(\log n)$ rounds, unless the 1-vs-2 cycles conjecture is false. This is true even on…
We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…
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…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. The tighter characteristic reduces the search…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
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…