Merge pull request #9 from JuliaOptimizationVariationalAnalysis/add-prg

1st commit prg

Author: tmigot

src/VariationalInequalitySolver.jl

@@ -76,9 +76,6 @@ function project!(model::NLSVIModel, d::AbstractVector{T}, Px::AbstractVector{T}
 end
 
 include("solvers/projectionVI.jl")
-#=
-include("projector/ProjNLP.jl")
-include("solvers/penalizedVI.jl")
-=#
+include("solvers/projected_reflected_gradient.jl")
 
 end

src/solvers/projected_reflected_gradient.jl

@@ -0,0 +1,39 @@
+"""
+> Yura Malitsky. Projected reflected gradient methods for monotone variational inequalities. 
+> SIAM Journal on Optimization, 25(1):502–520, 2015.
+"""
+function ProjectedReflectedGradientVI(stp::AbstractStopping; rho0::Float64 = 0.5)
+    xk = stp.current_state.x
+    xkp = similar(xk)
+    yk  = copy(xk)
+    rho = rho0
+    Fx = similar(xk)
+  
+    OK = update_and_start!(stp)
+    while !OK
+      abcresidual!(stp.pb, xk, rho, yk, Fx)
+      project!(stp.pb, Fx, xk) # possible failure here
+      yk .= 2 .* xkp .- xk
+  
+      if norm(xk - xkp, Inf) < stp.meta.atol * rho
+        stp.meta.optimal = true
+      end
+      OK = update_and_stop!(stp, x = xk)
+    end
+  
+    return xk
+  end
+  
+export ProjectedReflectedGradientVI
+
+function ProjectedReflectedGradientVI(model::AbstractVIModel, x0::AbstractVector; rho0::Float64 = 0.5, kwargs...)
+  stp = GenericStopping(model, x0; kwargs...)
+  return ProjectedReflectedGradientVI(stp, rho0 = rho0)
+end
+
+function abcresidual!(model, xk, rho, yk, Fx) # xk - rho * F(yk)
+  residual!(model, yk, Fx)
+  Fx .*= -rho
+  Fx .+= xk
+  return Fx
+end

src/solvers/projectionVI.jl

@@ -17,17 +17,16 @@ function ProjectionVI(stp::AbstractStopping; rho0::Float64 = 0.5)
   xkp = similar(xk)
   rho = rho0
   Fx = similar(xk)
-  abresidual!(stp.pb, xk, rho, Fx)
 
   OK = update_and_start!(stp)
   while !OK
     abresidual!(stp.pb, xk, rho, Fx)
-    project!(stp.pb, Fx, xkp) # possible failure here
+    project!(stp.pb, Fx, xk) # possible failure here
 
     if norm(xk - xkp, Inf) < stp.meta.atol * rho
       stp.meta.optimal = true
     end
-    OK = OK || update_and_stop!(stp, x = xk)
+    OK = update_and_stop!(stp, x = xk)
   end
 
   return xk

test/runtests.jl

@@ -9,7 +9,9 @@ Random.seed!(1234)
   vi = NLSVIModel(nls)
   xr = rand(2)
   @test project(vi, xr) == xr
-  sol = ProjectionVI(vi, xr)
+  sol1 = ProjectionVI(vi, xr)
+  sol2 = ProjectedReflectedGradientVI(vi, xr)
+  @show sol1, sol2
 end
 
 @testset "Test API AbstractVIModel" begin