Convex.jl <https://github.com/JuliaOpt/Convex.jl> is a Julia library for mathematical programming that makes it easy to formulate and fast to solve nonlinear convex optimization problems. Convex.jl <https://github.com/JuliaOpt/Convex.jl> is a member of the JuliaOpt <https://github.com/JuliaOpt> umbrella group and can use (nearly) any solver that complies with the MathProgBase interface, including Mosek <https://github.com/JuliaOpt/Mosek.jl>, Gurobi <https://github.com/JuliaOpt/gurobi.jl>, ECOS <https://github.com/JuliaOpt/ECOS.jl>, SCS <https://github.com/JuliaOpt/SCS.jl>, and GLPK <https://github.com/JuliaOpt/GLPK.jl>.
Here's a quick example of code that solves a non-negative least-squares problem. using Convex # Generate random problem data m = 4; n = 5 A = randn(m, n); b = randn(m, 1) # Create a (column vector) variable of size n x 1. x = Variable(n) # The problem is to minimize ||Ax - b||^2 subject to x >= 0 problem = minimize(sum_squares(A * x + b), [x >= 0]) solve!(problem) We could instead solve a robust approximation problem by replacing sum_squares(A * x + b) by sum(norm(A * x + b, 1)) or sum(huber(A * x + b)); it's that easy. Convex.jl <https://github.com/JuliaOpt/Convex.jl> is different from JuMP <https://github.com/JuliaOpt/JuMP.jl> in that it allows (and prioritizes) linear algebraic and functional constructions in objectives and constraints (like max(x,y) < A*z). Under the hood, it converts problems to a standard conic form, which requires (and certifies) that the problem is convex, and guarantees global optimality of the resulting solution.
