SPGBox.jl
SPGBox.jl is a pure-Julia implementation of the Spectral Projected Gradient Method for minimization in box constraints, as described in:
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)
How to install
julia> using Pkg
julia> Pkg.add("SPGBox")
or, more concisely,
julia> ] add SPGBox
Quick usage example
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 provide d as described here). Use spgbox
, to internaly copy the x
array and not mutate it.