I'm personally very pleased to see this. The JuMP team has worked closely with the Convex.jl team to make sure that we share a common infrastructure (through MathProgBase) to talk to solvers, and I don't think it's an exaggeration to say that this has resulted in an unprecedented level of solver interoperability. At this point I'm hard pressed to think of another platform besides Julia which lets you easily switch between AMPL/GAMS-style modeling (via JuMP) and DCP-style modeling (via Convex.jl) as you might experiment with different formulations of a problem.
On Wednesday, February 4, 2015 at 8:57:51 PM UTC-5, Elliot Saba wrote: > > This is so so cool, Madeleine. Thank you for sharing. I'm a huge fan of > DCP, ever since I took a convex optimization course here at the UW (which > of course featured cvx and Boyd's book) and seeing this in Julia makes me > smile. > -E > > On Wed, Feb 4, 2015 at 5:53 PM, Madeleine Udell <[email protected] > <javascript:>> wrote: > >> 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. >> > >
