Is it time for a native Julia LP(Simplex) solver?

baggepinnen · January 14, 2021, 9:11pm

I have some simple examples of exactly that here

baggepinnen/MonteCarloMeasurements.jl/blob/master/examples/autodiff_robust_opt.jl

# In this example we solve a robust linear programming problem using Optim. The problem is taken from [wikipedia](https://en.wikipedia.org/wiki/Robust_optimization#Example_1)

# $$\text{maximize}_{x,y} \; 3x+2y \quad \text{s.t}. x,y > 0, \quad cx+dy < 10 ∀ c,d ∈ P$$

# Where $c$ and $d$ are uncertain. We encode the constraint into the cost and solve it using 4 different algorithms


using MonteCarloMeasurements, Optim, ForwardDiff, Zygote

const c = 1 ∓ 0.1 # These are the uncertain parameters
const d = 1 ∓ 0.1 # These are the uncertain parameters
# In the cost function below, we ensure that $cx+dy > 10 \; ∀ \; c,d ∈ P$ by looking at the worst case
Base.findmax(p::AbstractParticles;dims=:) = findmax(p.particles,dims=:)
function cost(pars)
    x,y = pars
    -(3x+2y) + 10000sum(pars .< 0) + 10000*(maximum(c*x+d*y) > 10)
end

pars = [1., 1] # Initial guess
cost(pars)     # Try the cost function

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github.com

baggepinnen/MonteCarloMeasurements.jl/blob/master/examples/robust_controller_opt.jl

# In this script, we will design a PID controller by optimization. The system model has uncertain parameters, and we pay a price not only for poor performance of the closed-loop system, but also for a high variance in the performance. In addition to this, we place a constraint on the 90:th percentile of the maximum of the sensitivity function. This way, we will get a doubly robust controller as a result :)
# We start by defining the system and some initial controller parameters
using MonteCarloMeasurements, Optim, ControlSystems, Plots
using MonteCarloMeasurements: ∓
p = 1 ∓ 0.1
ζ = 0.3 ∓ 0.05
ω = 1 ∓ 0.1
P = tf([p*ω], [1, 2ζ*ω, ω^2])
w = exp10.(LinRange(-2,3,100))
params = [1,0.1,0.1]
Msc = 1.5 # Constraint on Ms

# We now define the cost function, which includes the constraint on the maximum sensitivity function
function cost(params)
    kp,ki,kd = params
    C = pid(kp=kp,ki=ki,kd=kd)
    G = feedback(P*C) # Closed-loop system
    S = 1/(1 + P*C)   # Sensitivity function
    local Gd
    try

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gobs · January 15, 2021, 9:14am

Cooooool! Makes me wish I had a reason to do this kind of stuff in my PhD but I’m already distracted enough as it is.