JuMP: A Modeling Language for Mathematical Optimization

Abstract

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to offer unique functionality while achieving performance on par with commercial modeling tools for standard tasks. In this work we will provide benchmarks, present the novel aspects of the implementation, and discuss how JuMP can be extended to new problem classes and composed with state-of-the-art tools for visualization and interactivity.

References in corpus (1)

• A Robust Approach to Chance Constrained Optimal Power Flow with Renewable Generation

Cited by in corpus (128)

• OSQP: An Operator Splitting Solver for Quadratic Programs
• A Tutorial on the Design, Experimentation and Application of Metaheuristic Algorithms to Real-World Optimization Problems
• Distributionally Robust Optimization: A Review
• Operational Research: Methods and Applications
• The software design of Gridap: a Finite Element package based on the Julia JIT compiler
• An optimal home energy management system for modulating heat pumps and photovoltaic systems
• Conformal field theories are magical
• An Exact Sequential Linear Programming Algorithm for the Optimal Power Flow Problem
• PowerModelsDistribution.jl: An Open-Source Framework for Exploring Distribution Power Flow Formulations
• Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
• A Survey on Energy Optimization Techniques in UAV-Based Cellular Networks: From Conventional to Machine Learning Approaches
• Data-Driven Distributionally Robust Optimal Power Flow for Distribution Systems
• Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia
• Chance Constraints for Improving the Security of AC Optimal Power Flow
• Extreme events in time series aggregation: A case study for optimal residential energy supply systems
• Sparse Regression: Scalable algorithms and empirical performance
• On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control
• State and Parameter Estimation for Natural Gas Pipeline Networks using Transient State Data
• COSMO: A conic operator splitting method for convex conic problems
• Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
• Planning low-carbon distributed power systems: Evaluating the role of energy storage
• Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization
• Polyhedral approximation in mixed-integer convex optimization
• A Reliability-Aware, Delay Guaranteed, and Resource Efficient Placement of Service Function Chains in Softwarized 5G Networks
• Convex Restriction of Power Flow Feasibility Sets
• Computational Bounds For Photonic Design
• Modelling and analysis of offshore energy hubs
• Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
• Fast Security-Constrained Optimal Power Flow through Low-Impact and Redundancy Screening
• Convolutional Neural Nets in Chemical Engineering: Foundations, Computations, and Applications
• Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions
• Linear Battery Models for Power Systems Analysis
• Adapting Datacenter Capacity for Greener Datacenters and Grid
• Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems
• PyPose: A Library for Robot Learning with Physics-based Optimization
• Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure
• Motion Planning and Control for Multi Vehicle Autonomous Racing at High Speeds
• Sparse Classification: a scalable discrete optimization perspective
• Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods
• Distributionally Robust Chance Constrained Programming with Generative Adversarial Networks (GANs)
• Iterative LP-based Methods for the Multiperiod Optimal Electricity and Gas Flow Problem
• Contract design in electricity markets with high penetration of renewables: A two-stage approach
• Topological metric detects hidden order in disordered media
• A computationally efficient Benders decomposition for energy systems planning problems with detailed operations and time-coupling constraints
• Electricity Market Equilibrium under Information Asymmetry
• A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl
• DISROPT: a Python Framework for Distributed Optimization
• Natural Gas Short-Term Operation Problem with Dynamics: A Rank Minimization Approach
• A fast algorithm for maximum likelihood estimation of mixture proportions using sequential quadratic programming
• Optimal Power Flow: An Introduction to Predictive, Distributed and Stochastic Control Challenges
• Dynamic QoS-Aware Traffic Planning for Time-Triggered Flows in the Real-time Data Plane
• Graph-Based Modeling and Decomposition of Energy Infrastructures
• Heuristic Methods and Performance Bounds for Photonic Design
• Semi-definite programming and quantum information
• PowerModelsRestoration.jl: An Open-Source Framework for Exploring Power Network Restoration Algorithms
• Diffusing-Horizon Model Predictive Control
• OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets
• Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems
• Comparison Between Robust and Stochastic Optimisation for Long-term Reservoir Operations Under Uncertainty
• A Hierarchical Optimization Architecture for Large-Scale Power Networks
• Contracts in Electricity Markets under EU ETS: A Stochastic Programming Approach
• Engineering spin-spin interactions with optical tweezers in trapped ions
• A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems
• Computational Framework for Behind-The-Meter DER Techno-Economic Modeling and Optimization -- REopt Lite
• Efficient Stochastic Programming in Julia
• A Computational Framework for Quantifying and Analyzing System Flexibility
• Strengthening the Group: Aggregated Frequency Reserve Bidding with ADMM
• $\mathrm{Aut}({\mathbb{F}}_5)$ has property $(T)$
• Dynamic locational marginal emissions via implicit differentiation
• Performance enhancements for a generic conic interior point algorithm
• Construction of quasi-potentials for stochastic dynamical systems: an optimization approach
• Online Learning for Network Constrained Demand Response Pricing in Distribution Systems
• Complete hierarchy for high-dimensional steering certification
• A Mixed-Integer Conic Programming Formulation for Computing the Flexibility Index under Multivariate Gaussian Uncertainty
• Beyond capacity: contractual form in electricity reliability obligations
• Analytical Uncertainty Propagation for Multi-Period Stochastic Optimal Power Flow
• Improved finite-size key rates for discrete-modulated continuous variable quantum key distribution under coherent attacks
• Hardware-aware Design of Multiplierless Second-Order IIR Filters with Minimum Adders
• A Bayesian framework for molecular strain identification from mixed diagnostic samples
• Design and implementation of a modular interior-point solver for linear optimization
• A unified approach to mixed-integer optimization problems with logical constraints
• Locating the source of forced oscillations in transmission power grids
• Unbalanced OPF Modelling for Mixed Monopolar and Bipolar HVDC Grid Configurations
• Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems
• Stability Properties of the Adaptive Horizon Multi-Stage MPC
• Automatic scenario generation for efficient solution of robust optimal control problems
• Impacts of Dynamic Line Ratings on the ERCOT Transmission System
• Computational Analysis of Impedance Transformations for Four-Wire Power Networks with Sparse Neutral Grounding
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Global Optimization via Optimal Decision Trees
• Brachistochrone on a Velodrome
• The lower bound of the network connectivity guaranteeing in-phase synchronization
• On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems
• Equitably allocating wildfire resilience investments for power grids: The curse of aggregation and vulnerability indices
• Self-induced glassy phase in multimodal cavity quantum electrodynamics
• Sequence of Polyhedral Relaxations for Nonlinear Univariate Functions
• Fair Allocation of Conflicting Items
• Measuring and Optimizing System Reliability: A Stochastic Programming Approach
• Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing
• Overlapping Schwarz Decomposition for Constrained Quadratic Programs
• A Hilbertian projection method for constrained level set-based topology optimisation
• Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization
• A Scalable Stochastic Programming Approach for the Design of Flexible Systems
• Dynamically adaptive networks for integrating optimal pressure management and self-cleaning controls
• Credible Interdiction for Transmission Systems
• A Stochastic Benders Decomposition Scheme for Large-Scale Stochastic Network Design
• Reducing urban traffic congestion due to localized routing decisions
• Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point
• Optimal day-ahead orders using stochastic programming and noise-driven RNNs
• AnyMOD.jl: A Julia package for creating energy system models
• Bounds and convex heuristics for bi-objective optimal experiment design in water networks
• Distributed nonconvex optimization for control of water networks with time-coupling constraints
• Designing a Framework for Solving Multiobjective Simulation Optimization Problems
• An integer programming model for the selection of pumped-hydro storage projects
• COMANDO: A Next-Generation Open-Source Framework for Energy Systems Optimization
• A Unifying Modeling Abstraction for Infinite-Dimensional Optimization
• Embedding Reservoirs in Industrial Models to Exploit their Flexibility
• A Julia Framework for Graph-Structured Nonlinear Optimization
• A Certifably Correct Algorithm for Generalized Robot-World and Hand-Eye Calibration
• Growth factors of orthogonal matrices and local behavior of Gaussian elimination with partial and complete pivoting
• Cost-Sensitive Best Subset Selection for Logistic Regression: A Mixed-Integer Conic Optimization Perspective
• Volt-VAr-Watt Optimization in Four-Wire Low-Voltage Networks: Exact Nonlinear Models and Smooth Approximations - Extended Version
• Exact Solutions to a Class of Constrained Optimal Control Problems via Lossless Convexification for Digital Control
• A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development
• Uncovering expert objectives in production planning via inverse optimization: An industrial case study
• Performance Bounds for Quantum Feedback Control
• Risk-averse decision strategies for influence diagrams using rooted junction trees
• On the Impact of Voltage Unbalance on Distribution Locational Marginal Prices