mlubin

There are four different levels at which users may interact with LP solvers (top to bottom):

• Algebraic modeling languages such as MathProg.jl
• Matlab-style linprog functions, provide problem as input and retrieve solution in one function call. Maybe put this in Optim.jl.
• Standard low-level interface. This is a state-based interface with a solver object where the user may dynamically add and remove variables and constraints, repeatedly resolve the problem with hotstarts (important for decomposition algorithms), etc. Inspired by COIN-OR's OSI project, but hopefully we can improve on some of their mistakes.
• Solver-specific low-level interface. Typically a lightweight wrapper around the solver's C interface. Names should follow the solver's convention.

Implementers of solver interfaces (or solvers written in Julia) are responsible for providing the standard low-level interface (not linprog). The linprog interface will be built on top of the standard low-level interface.

mlubin

function genF(Q)
    f(x) = (1/2)*dot(x,Q*x)
    fgrad(x) = Q*x
    return f, fgrad
end

function gradDescent(f, fgrad, startX)

    const stepsize = 1.0
    const sigma = 0.1

mlubin

import Optim

function clogit_ll{R}(coeff::Vector{R}, x1, x2, x3, x4, x5, x6,
		    y1, y2, y3, y4, y5, y6,
		    T, nObs, nVar)

    llit = zero(R)

    for i=1:nObs
        for t=1:T

mlubin

function squareroot(x)
    it = x
    while abs(it*it - x) > 1e-13
        it = it - (it*it-x)/(2it)
    end
    return it
end

function time_sqrt(x)
    const num_iter = 100000

mlubin

mlubin

mlubin

using Convex
using ECOS
using SCS
using ConicNonlinearBridge
using Ipopt
x1 = Variable(1)
x2 = Variable(1)
x3 = Variable(1)
x4 = Variable(1)
x5 = Variable(1)

mlubin

using Mosek, MathProgBase

I = [1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,32,33,33,34,34,35,36,37,38,39,40]
J = [14,10,15,11,16,12,13,18,1,21,2,24,3,19,2,22,4,25,5,20,3,23,5,26,6,17,13,17,13,14,15,16,17,18,19,20,21,22,23,24,25,26,7,10,8,11,9,12,1,2,3,4,5,6]
V = [1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,1.0,1.0,-1.0,1.0,1.0,1.0,-1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0]
b = [-0.6088331477422722,-0.02852197818671054,-0.9016074145524158,0.4999165215049682,-0.025485683857737418,-0.07276320066249353,0.056565030662414396,-0.07276320066249353,-0.3319954143963322,0.3286736785015988,0.056565030662414396,0.3286736785015988,-0.43682537007384287,1.0516057442061533,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,18.999999999999996,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
var_cones = Any[(:SDP,1:6),(:NonNeg,[13,17

mlubin

using JuMP, Mosek, FactCheck

sdp_solvers = [MosekSolver(LOG=0)]
include(Pkg.dir("JuMP","test","data","robust_uncertainty.jl"))

facts("[sdp] Robust uncertainty example") do
for solver in sdp_solvers
context("With solver $(typeof(solver))") do
    R = 1
    d = 3

mlubin

     pcost       dcost       gap    pres   dres
 0:  3.8500e+03  3.9338e+03  2e+03  1e+00  1e+00
 1:  2.0645e+03  2.1700e+03  2e+03  1e+00  1e+00
 2:  4.0064e+02  5.8278e+02  2e+03  1e+00  1e+00
 3:  2.5441e+02  6.9543e+02  2e+03  9e-01  9e-01
 4:  4.3080e+02  1.2381e+03  1e+03  8e-01  8e-01
 5:  6.7652e+02  2.0939e+03  1e+03  7e-01  7e-01
 6:  8.9445e+02  2.8259e+03  1e+03  6e-01  6e-01
 7:  1.2857e+03  4.1114e+03  1e+03  6e-01  6e-01
 8:  1.6758e+03  5.4303e+03  1e+03  5e-01  5e-01