Optimize the product of a matrix and scalar

General Usage
1

This code:

function objective(xy)
    x, y = xy
    return (3y^2*x + x^3-m3)*W*(3y^2*x + x^3-m3)
end

xy0 = [x, y]
result = optimize(objective, xy0, NelderMead())
println(result)

minimizer = result.minimizer
x, y = minimizer
println("x = ", x)
println("y = ", y)

where W=:

2×2 Matrix{Float64}:
 2.87989e-6  9.85217e-7
 9.85217e-7  4.4135e-7

Returns the error:

MethodError: Cannot `convert` an object of type Matrix{Float64} to an object of type Float64
Closest candidates are:
  convert(::Type{T}, !Matched::Base.TwicePrecision) where T<:Number at twiceprecision.jl:273
  convert(::Type{T}, !Matched::AbstractChar) where T<:Number at char.jl:185
  convert(::Type{T}, !Matched::CartesianIndex{1}) where T<:Number at multidimensional.jl:130
  ...

I seem to be able to multiply a scalar by a matrix by a scalar normally:

5*W*5

returns:

2×2 Matrix{Float64}:
 7.19973e-5  2.46304e-5
 2.46304e-5  1.10338e-5

Does anyone know why it does not work within the Optim environment, and how to fix it? Thank you!

2

The objective function returns a matrix when it should return a scalar.

1 Like
3

If 5*W*5 truly is what you would like to do, you might save some work by instead computing 5^2*W. But since you are treating the result as an objective function, you likely intend to compute an inner product?

3 Likes
4

Besides being lazy with W in the following, I needed also a value for m3, but this for example works (assuming your terms with + are vectors

using Optim
	m3 = 0.3
	function objective(xy)
    	x, y = xy
    	return [3y^2*x, x^3-m3]'*W*[3y^2*x, x^3-m3]
	end
	W = [1.0 1.0; 0.0 1.0]
	x = 0.0
	y = 0.0
	xy0 = [x, y]
	result = optimize(objective, xy0, NelderMead())
	println(result)

	minimizer = result.minimizer
	x, y = minimizer
	println("x = ", x)
	println("y = ", y)

returns

 * Status: success

 * Candidate solution
    Final objective value:     1.283678e-09

 * Found with
    Algorithm:     Nelder-Mead

 * Convergence measures
    √(Σ(yᵢ-ȳ)²)/n ≤ 1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    46
    f(x) calls:    92

x = 0.6694227744863399
y = -0.004499203729393773