Bridging Continuous and Discrete Optimization in Julia
Abstract
Julia's strength in mathematical computation and high performance makes it a popular choice across scientific fields, mostly due to its focus on mathematics in a broad sense and execution performance. It is a language of choice to implement new numerical algorithms, but it really shines in modelling for optimisation thanks to JuMP.jl and MathOptInterface.jl.
These libraries are, first and foremost, made for mathematical optimisation (linear, mixed-integer, conic, etc.), yet they are now generic enough to support more paradigms, such as constraint programming. This talk will introduce the basic principles behind the current implementation of JuMP.jl and explain why and how they are very good matches for modelling using constraint programming… and solving using any kind of mixed-integer-programming solver.
Constraint-programming solvers can also be implemented using linear programming, in a great collaboration between discrete and continuous optimisation. This talk will briefly explain the connection and its implementation in Google’s CP-SAT, a leading, award-winning constraint solver that uses linear programs in its solving process — a solver that will soon be available in Julia too.
These libraries are, first and foremost, made for mathematical optimisation (linear, mixed-integer, conic, etc.), yet they are now generic enough to support more paradigms, such as constraint programming. This talk will introduce the basic principles behind the current implementation of JuMP.jl and explain why and how they are very good matches for modelling using constraint programming… and solving using any kind of mixed-integer-programming solver.
Constraint-programming solvers can also be implemented using linear programming, in a great collaboration between discrete and continuous optimisation. This talk will briefly explain the connection and its implementation in Google’s CP-SAT, a leading, award-winning constraint solver that uses linear programs in its solving process — a solver that will soon be available in Julia too.
