GDP
This optimizer should not be used: Use WallE instead.
Bounding Box Optimizer for large problems where the optimal solution lies on the boundary. The algorithm is a modified Steepest Descent projecting infeasible variables to the boundary of the feasible design space (defined by the side constraints ci and cs) and with no line-search. The objective function is used when the gradient is the same during two consecutive iterations..
Example
using GDP
# Objective function
function f(x)
100*(x[2]-x[1]^2)^2+(x[1]-1)^2
end
# Gradient of objective function
function df(x)
df1 = 2.0*(x[1]-1)-400*x[1]*(x[2]-x[1]^2)
df2 = 200.0*(x[2]-x[1]^2)
return [df1 ; df2]
end
# Initial point
x0 = [0.0 ; 3.0]
# Side constraints
ci = [-Inf ; 0.5]
cs = [0.8 ; Inf]
# Call optimizer
options = GDP.Init()
options["NITER"] = 10_000
output = GDP.Solve(f,df,x0,ci,cs,options)
# Recovering solution
x_opt = output["RESULT"]
flag_converged = output["CONVERGED"]
opt_norm = output["NORM"]
number_iter = output["NITER"]
Default input options are
"NITER"=>1000
"TOL_NORM"=>1E-6
"ALPHA_0"=>1E-10
"FACTOR_Z"=>0.99
"MIN_STEP"=>1E-12
"SHOW"=>true
"WITH_LS"=>false
where NITER is the maximum number of iterations, TOL_NORM is the tolerance to assess convergence, ALPHA_0 is the initial step length (do no change unless you read the theory), FACTOR_Z (do no change unless you read the theory), MIN_STEP is the minimum step used to skip the loop (if this value is used for the last 5 iterations) and SHOW prints information or, if false, runs silently. If WITH_LS is true, the step is obtained with a projected Armijo's LS.
Default output options are
"RESULT"=>x
"CONVERGED"=>flag_conv
"NORM"=>norm_D
"ITERS"=>counterwhere RESULT contains the vector of design variables, CONVERGED is true if all the first order conditions are met, NORM is the norm of the gradient of free (unconstrained) variables and ITERS is the effective number of iterations.