convert MATLAB optimise function to julia - matlab

Question

I am trying to convert a Matlab fmincon optimisation function to julia.
but without much luck.
I think NLopt or IPopt can be used.
the default examples work but when i try to change the values it doesnt seem to iterate.
using NLopt
count = 0 # keep track of # function evaluations
function myfunc(x::Vector, grad::Vector)
if length(grad) > 0
grad[1] = 0
grad[2] = 0.5/sqrt(x[2])
end
global count
count::Int += 1
println("f_$count($x)")
sqrt(x[2])
end
function myconstraint(x::Vector, grad::Vector, a, b)
if length(grad) > 0
grad[1] = 3a * (a*x[1] + b)^2
grad[2] = -1
end
(a*x[1] + b)^3 - x[2]
end
opt = Opt(:LD_MMA, 2)
lower_bounds!(opt, [-Inf, 0.])
xtol_rel!(opt,1e-4)
min_objective!(opt, myfunc)
inequality_constraint!(opt, (x,g) -> myconstraint(x,g,2,0), 1e-8)
inequality_constraint!(opt, (x,g) -> myconstraint(x,g,-1,1), 1e-8)
(minf,minx,ret) = optimize(opt, [1.234, 5.678])
println("got $minf at $minx after $count iterations (returned $ret)")
This one works fine. it gives 2 results and 11 iterations
using NLopt
count = 0 # keep track of # function evaluations
function myfunc(x)
x[1]^2 + 5*x[2] - 3
end
function myconstraint(x)
100*x[1] + 2000*x[2] == 100
end
opt = Opt(:LD_MMA, 2)
lower_bounds!(opt, [0, 0])
upper_bounds!(opt,[10,5])
xtol_rel!(opt,1e-10)
min_objective!(opt, myfunc);
inequality_constraint!(opt, (x) -> myconstraint(x), 1e-10)
(minf,minx,ret) = optimize(opt, [0.1,0.1])
This doesnt work, It just gives a result and 0 iterations
using NLopt
count = 0 # keep track of # function evaluations
function myfunc(x::Vector, grad::Vector)
x[1]^2 + 5*x[2] - 3
end
function myconstraint(result::Vector, x::Vector, grad::Vector)
100*x[1] + 2000*x[2] == 100
end
opt = Opt(:LD_MMA, 2)
lower_bounds!(opt, [0., 0.])
upper_bounds!(opt, [10.,5.])
xtol_rel!(opt,1e-4)
min_objective!(opt, myfunc)
inequality_constraint!(opt, (x,g) -> myconstraint(x), 1e-8)
(minf,minx,ret) = optimize(opt, [0., 0.])#even with [5.,10.]
this just gives me a result and 0 iterations.
anyone any idea what i a doing wrong?

Answer 1

I'm having a tough time reconstructing what you've done based on the comment marathon, so instead I thought I would just provide code indicating how I would have solved this problem. Note, the following code assumes your inequality constraint is 100*x[1] + 2000*x[2] <= 100:
using NLopt
function myfunc(x::Vector{Float64}, grad::Vector{Float64})
if length(grad) > 0
grad[1] = 2 * x[1]
grad[2] = 5
end
xOut = x[1]^2 + 5*x[2] - 3
println("Obj func = " * string(xOut))
return(xOut)
end
function myconstraint(x::Vector{Float64}, grad::Vector{Float64})
if length(grad) > 0
grad[1] = 100
grad[2] = 2000
end
xOut = 100*x[1] + 2000*x[2] - 100
println("Constraint val = " * string(xOut))
return(xOut)
end
opt = Opt(:LD_MMA, 2)
lower_bounds!(opt, [0, 0])
upper_bounds!(opt,[10,5])
xtol_rel!(opt,1e-10)
min_objective!(opt, myfunc);
inequality_constraint!(opt, myconstraint, 1e-10)
(minf,minx,ret) = optimize(opt, [0.1,0.1])
There are three main differences between my code and yours:
I've explicitly included the gradient function updates. This will make the convergence routine more efficient for any gradient-based algorithm (of which MMA is one).
I'm printing out the values of my objective function and constraint function at each step. This is useful for debugging purposes, and to get some idea of what is happening under the hood.
I've made it very clear in my code that the return value from my constraint function is f(x), where the constraint is defined by the equation f(x) <= 0. This is the appropriate syntax for use with NLopt.
You stated in the comments that you are getting an error when you try to change inequality_constraint! to equality_constraint!. This is because your algorithm of choice (MMA) only supports inequality constraints. A description of the NLopt algorithms can be found here. Note:
only MMA and SLSQP support arbitrary nonlinear inequality constraints, and only SLSQP supports nonlinear equality constraints
So, switch your algorithm to :LD_SLSQP, and voila, you can now switch your inequality constraint to an equality constraint.