Related papers: MPAX: Mathematical Programming in JAX

Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is…

Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…

This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and…

Basic Linear Algebra Subprograms (BLAS) are a set of low level linear algebra kernels widely adopted by applications involved with the deep learning and scientific computing. The massive and economic computing power brought forth by the…

This work introduces ParamRF: a Python library for efficient, parametric modelling of radio frequency (RF) circuits. Built on top of the next-generation computational library JAX, as well as the object-oriented wrapper Equinox, the…

We present a novel, JAX-powered implementation of a parametric component-separation method for CMB polarization data, explicitly designed to handle spatially varying foreground Spectral Energy Distributions (SEDs). The approach models this…

Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…

We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the…

SymJAX is a symbolic programming version of JAX simplifying graph input/output/updates and providing additional functionalities for general machine learning and deep learning applications. From an user perspective SymJAX provides a la…

Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical…

We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…

We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an…

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…

In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…

In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…

Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the singular integrals encountered in the evaluation of layer potentials. It exploits the smoothness of the layer potential by forming locally-valid…

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…

Machine Reassignment is a challenging problem for constraint programming (CP) and mixed-integer linear programming (MILP) approaches, especially given the size of data centres. The multi-objective version of the Machine Reassignment Problem…

We propose a mixed-integer quadratic programming (QP) solver that is suitable for use in embedded applications, for example, hybrid model predictive control (MPC). The solver is based on the branch-and-bound method, and uses a recently…

This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…