Optimization

Mathematical Optimization packages in Julia.

Organizations

• Julia Smooth Optimizers
• JuMP-dev
• Julia for Dynamic Optimization
• JuliaNLSolvers
• SciML

JuMP

JuMP.jl : Modeling Mathematical Optimization (linear, mixed-integer, conic, semidefinite, nonlinear).

• JuDO.jl: solving optimal control problems. See also
• MathOptInterface.jl: An abstraction layer for mathematical optimization solvers.
• PolyJuMP.jl : A JuMP extension for Polynomial Optimization.
• Progradio.jl : Projected Gradient Optimization. Julia Con 2023 video
• SDDP.jl: A JuMP extension for Stochastic Dual Dynamic Programming.
• StructJuMP.jl : A block-structured optimization framework for JuMP.
• SumOfSquares.jl : Sum of Squares Programming for Julia.

External solvers

Some of them require paid license to work.

• AmplNLWriter.jl : an interface between MathOptInterface.jl and AMPL-enabled solvers.
• BARON.jl : A wrapper for the BARON mixed-integer nonlinear programming solver.
• Cbc.jl : Interface to the Coin-OR Cbc solver for mixed-integer programming.
• Clp.jl : Interface to the Coin-OR Linear Programming solver (CLP)
• CPLEX.jl : An interface for using IBM’s CPLEX Optimizer™ from the Julia language.
• CSDP.jl : Julia wrapper to CSDP semidefinite programming solver.
• ECOS.jl : Julia wrapper for the ECOS conic optimization solver.
• GLPK.jl : GLPK wrapper module for Julia.
• Gurobi.j : a Julia interface for the commercial Gurobi Optimizer.
• Ipopt.jl : Julia interface to the Ipopt nonlinear solver.
• KNITRO.jl : Julia interface for KNITRO solver.
• Mosek.jl : Interface to the Mosek solver in Julia. The interface to JuMP is MosekTools.jl
• NEOSServer.jl : A Julia interface for the NEOS Optimisation Server.
• SCS.jl : Julia Wrapper for SCS.
• Xpress.jl : A Julia interface for the FICO Xpress solver.

Optimization.jl

Optimization.jl : brings together all of the optimization packages it can find, local and global, into one unified Julia interface. The following list comes from it README.

• OptimizationBBO: for BlackBoxOptim.jl : An experimental, work-in-progress global optimization framework for Julia, supporting both multiand single-objective optimization problems, focused on (meta-)heuristic/stochastic algorithms (DE, PSO, CMA-ES etc).
• OptimizationEvolutionary: for Evolutionary.jl : Evolutionary & genetic algorithms for Julia. Wikipedia: Genetic algorithm
• OptimizationGCMAES for  GCMAES.jl: Gradient-based Covariance Matrix Adaptation Evolutionary Strategy for Real Blackbox Optimization.
• OptimizationIpopt for Ipopt.jl
• OptimizationLBFGSB for LBFGSB.jl: Julia wrapper for L-BFGS-B Nonlinear Optimization Code.
• OptimizationMadNLP for MadNLP.jl: a solver for nonlinear programming with GPU support
• OptimizationManopt for Manopt.jl : Optimization on Manifolds in Julia.
• OptimizationMetaheuristics for Metaheuristics.jl : High performance metaheuristics for global optimization.
• OptimizationMOI for MathOptInterface.jl
• OptimizationMultistartOptimization for MultistartOptimization.jl
• OptimizationNLopt for NLopt.jl : Package to call the NLopt nonlinear-optimization library from the Julia language.
• OptimizationNLPModels for NLPModels.jl
• OptimizationNOMAD for NOMAD.jl: a Julia interface for NOMAD, which is a C++ implementation of the Mesh Adaptive Direct Search algorithm (MADS), designed for difficult blackbox optimization problems.
• OptimizationOptimJL for Optim.jl : Univariate and multivariate optimization solvers in Julia.
• OptimizationOptimisers for FluxML’s Optimisers.jl.
• OptimizationPRIMA for  PRIMA.jl: a Julia interface to the PRIMA library.
• OptimizationQuadDIRECT for QuadDIRECT.jl: Global optimization without derivatives.
• OptimizationSophia for Sophia optimizer (second-order stochastic optimizer).
• OptimizationSpeedMapping for SpeedMapping.jl: General fixed point mapping acceleration and optimization in Julia.

Linear Programming and Optimization

Wikipedia: Linear Programming-Optimization

• PiecewiseLinearOpt.jl : Optimizing over piecewise linear functions.
• Tulip.jl : is an open-source interior-point solver for linear optimization, written in pure Julia. It implements the homogeneous primal-dual interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems.

Nonlinear Programming

Wikipedia: Nonlinear Programming:  some of the constraints are not linear equalities or the objective function is not a linear function.

• Convex.jl : Disciplined Convex Programming (DCP).
• EAGO.jl : A development environment for robust and global optimization. EAGO stands for Easy-Advanced Global Optimization.
• MadNLP.jl: a solver for nonlinear programming with GPU support

Julia smooth solvers

OptimizationProblems.jl: This package provides a collection of optimization problems in JuMP and ADNLPModels syntax.

• AmplNLReader.jl : A Julia Interface to AMPL.
• CUTEst.jl : Julia interface for CUTEst, a repository of constrained and unconstrained nonlinear programming problems for testing and comparing optimization algorithms.
• HSL.jl : Julia interface to the HSL Mathematical Software Library.
• JSOSuite.jl : accessing all the solvers available in the JuliaSmoothOptimizers organization.
• LinearOperators.jl : Linear Operators for Julia. Operators behave like matrices but are defined by their effect when applied to a vector.
• NLPModels.jl : Data Structures for non-linear programming (NLP) problems in Julia.

Misc

• Hyperopt.jl : A package to perform hyperparameter optimization. Currently supports random search, Latin hypercube sampling and Bayesian optimization.
• InfiniteOpt.jl : An interface for infinite-dimensional optimization problems. e.g. stochastic programming, dynamic programming, space-time optimization. See also the YouTube video.
• IntervalConstraintProgramming.jl : Calculates the feasible region for a set of real-valued inequalities with Julia.
• MetaheuristicsAlgorithms.jl : a collection of Metaheuristics Algorithms written in Julia. YT video
• OSQP.jl : A Julia wrapper for the Operator Splitting Quadratic Program (OSQP) solver, a numerical optimization package.
• SMM.jl : Simulated Method of Moments for Julia.