fminbox_nogradient.jl

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   _       _ _(_)_     |  Documentation: https://docs.julialang.org
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  | | |_| | | | (_| |  |  Version 1.0.2 (2018-11-08)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
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julia> using Optim

julia> function rosenbrock(x::Vector)
         return (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
       end
rosenbrock (generic function with 1 method)

julia> optimize(rosenbrock, fill(-1.0,2), fill(1.0, 2), rand(2), Fminbox(GradientDescent()))
Results of Optimization Algorithm
 * Algorithm: Fminbox with Gradient Descent
 * Starting Point: [0.48326410702842115,0.4690378993320623]
 * Minimizer: [0.9999999839553474,0.9999999678607662]
 * Minimum: 2.576802e-16
 * Iterations: 21
 * Convergence: true
   * |x - x'| ≤ 0.0e+00: false 
     |x - x'| = 2.06e-08 
   * |f(x) - f(x')| ≤ 0.0e+00 |f(x)|: false
     |f(x) - f(x')| = 1.48e+00 |f(x)|
   * |g(x)| ≤ 1.0e-08: true 
     |g(x)| = 9.99e-09 
   * Stopped by an increasing objective: false
   * Reached Maximum Number of Iterations: false
 * Objective Calls: 577760
 * Gradient Calls: 577760

julia> optimize(rosenbrock, fill(-1.0,2), fill(1.0, 2), rand(2), Fminbox(BFGS()))
Results of Optimization Algorithm
 * Algorithm: Fminbox with BFGS
 * Starting Point: [0.5506698212274612,0.8757619596191757]
 * Minimizer: [0.9999999896473769,0.9999999792757609]
 * Minimum: 1.072129e-16
 * Iterations: 6
 * Convergence: true
   * |x - x'| ≤ 0.0e+00: false 
     |x - x'| = 3.10e-07 
   * |f(x) - f(x')| ≤ 0.0e+00 |f(x)|: false
     |f(x) - f(x')| = 2.05e+02 |f(x)|
   * |g(x)| ≤ 1.0e-08: true 
     |g(x)| = 3.80e-09 
   * Stopped by an increasing objective: false
   * Reached Maximum Number of Iterations: false
 * Objective Calls: 536
 * Gradient Calls: 536