some comments on initial condition, included possible algorithms

optim_mixture.jl

@@ -262,7 +262,6 @@ function plot_result_mixture_1(X::Vector{Float64}, N::Int, M::Int, m::Int)
     GLM.Axis(fig[1, i], aspect=aspect)
   end
 
-
   n = Int(sqrt(N))
 
   # Component density
@@ -287,7 +286,13 @@ function optim(algo::Symbol=:LD_MMA)
   N::Int, M::Int = size(Y)
   m::Int = 2
 
-  X::Vector{Float64} = fill(0.5, (N + M) * m)
+  # Initial choice of X
+  # it seems that:
+  # * ∇E(0) = 0
+  # X::Vector{Float64} = zeros((N + M) * m)
+  # * choosing X = 0.5 and BFGS yields a relatively quick convergence to two identical components
+  # X::Vector{Float64} = fill(0.5, (N + M) * m)
+  X::Vector{Float64} = 0.5 .+ 0.1 * rand((N + M) * m)
   ∇E::Vector{Float64} = zeros((N + M) * m)
   tmp = zeros(size(Y))
 
@@ -311,13 +316,31 @@ function optim(algo::Symbol=:LD_MMA)
 
   res = NLopt.optimize(opt, X)
 
-  return res
+  @show opt
+
+  return res, opt
 end
 
 
 end # module
 
-res = OptimMixture.optim(:LD_LBFGS);
+# possible algorithms from NLopt
+#    LD_LBFGS_NOCEDAL
+#    LD_LBFGS
+#    LD_VAR1
+#    LD_VAR2
+#    LD_TNEWTON
+#    LD_TNEWTON_RESTART
+#    LD_TNEWTON_PRECOND
+#    LD_TNEWTON_PRECOND_RESTART
+#    LD_MMA
+#    LD_AUGLAG
+#    LD_AUGLAG_EQ
+#    LD_SLSQP
+#    LD_CCSAQ
+
+res, opt = OptimMixture.optim(:LD_LBFGS);
+# res, opt = OptimMixture.optim(:LD_TNEWTON)
 OptimMixture.plot_result_mixture_1(res[2], 512 * 512, 32, 2)
 # OptimMixture.benchmark();
 # OptimMixture.test_E(512 * 512, 32, 2)