SPGBox.jl

Implements the Spectral Projected Gradient Method for minimization with box constraints.

Algorithm reference:

E. G. Birgin, J. M. Martínez and M. Raydan, "Nonmonotone spectral projected gradient methods on convex sets", SIAM Journal on Optimization 10, pp. 1196-1211, 2000. LINK

The complete documentation can be found at: https://m3g.github.io/SPGBox.jl

julia> using Pkg

julia> Pkg.add("SPGBox")

or, more concisely,

julia> ] add SPGBox

Define the function to compute the objective function and the gradient, for example with:

julia> f(x) = x[1]^2 + x[2]^2

julia> function g!(g,x)
           g[1] = 2*x[1]
           g[2] = 2*x[2]
       end

And the objective function can be minimized with optional box bounds. Here, with a lower bound of 2 for the first variable:

julia> x = 2 .+ rand(2)

julia> spgbox!(f,g!,x,lower=[2.,-Inf])

 SPGBOX RESULT: 

 Convergence achieved. 

 Final objective function value = 4.0
 Sample of best point = Vector{Float64}[ 2.0, 0.0]
 Projected gradient norm = 0.0

 Number of iterations = 3
 Number of function evaluations = 3

The spgbox! function mutates the content of the input x vector (and will not allocate anything if the auxiliary vectors are provided as described here). Use spgbox, to internaly copy the x array and not mutate it.