Add_minimalsurface

src/ADNLPProblems/minimalsurface.jl

@@ -0,0 +1,105 @@
+using Plots
+using ADNLPModels, NLPModels, NLPModelsIpopt, DataFrames, LinearAlgebra, Distances, SolverCore, PyPlot
+
+function minimalsurface(; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+
+    # domain definition
+    xmin = T(0.)
+    xmax = T(1.)
+    ymin = T(0.)
+    ymax = T(1.)
+
+    # Definition of the mesh
+    nx = 20 # number of points according to the direction x
+    ny = 20 # number of points according to the direction y
+
+
+    x_mesh = LinRange(xmin, xmax, nx) # coordinates of the mesh points x
+    y_mesh = LinRange(ymin, ymax, ny) # coordinates of the mesh points y
+
+    v_D = zeros(nx,ny) # Surface matrix initialization
+    for i in 1:nx
+        for j in 1:ny
+            v_D[i, j] = T(1 - (2 * x_mesh[i] - 1)^2)
+        end 
+    end  
+
+
+    function Objective(v)
+        v_reshape = reshape(v, (nx, ny)) # vector to matrix conversion
+        hx = T(1/nx)  # step on the x axis
+        hy = T(1/ny)  # step on the y axis
+        S = T(0.) # sum initialization
+        # Calculation of the gradient according to x
+        for i in 1:nx
+            for j in 1:ny
+                if i == 1
+                    gi = T((v_reshape[i+1, j] - v_reshape[i, j])/hx)
+                elseif i == nx
+                    gi = T((v_reshape[i, j] - v_reshape[i-1, j])/hx)
+                else 
+                    gi = T((v_reshape[i+1, j] - v_reshape[i, j])/(2 * hx))
+                end 
+        # Calculation of the gradient according to x
+                if j == 1
+                    gj = T((v_reshape[i, j+1] - v_reshape[i, j])/hy)            
+                elseif j == ny
+                    gj = T((v_reshape[i, j] - v_reshape[i, j-1])/hy) 
+                else 
+                    gj = T((v_reshape[i, j+1] - v_reshape[i, j])/(2 * hy)) 
+                end 
+
+                s = T(hx * hy * (sqrt(1 + (gi^2) +(gj)^2))) # Approximation of the derivative with the method of rectangles
+                S = S + s # Update the value of S
+            end
+        end
+        return(S)
+    end 
+
+    function constraints(v)
+        v_reshape = reshape(v, (nx, ny)) # vector to matrix conversion
+        c = similar(v_reshape, nx*ny + 2*(nx +ny)) # creating a constraint vector
+        index = 1
+        v_L = zeros(T, nx,ny) # Creation of an obstacle called v_L
+        for i in 1:nx
+            for j in 1:ny
+                if norm(x_mesh[i]-(1/2)) ≤ 1/4 && norm(y_mesh[j]-(1/2)) ≤ 1/4
+                    v_L[i, j] = T(1.) # Update the value of v_L according to the values ​​of x and y
+                end
+            end 
+        end  
+        for i in 1:nx
+            for j in 1:ny
+                c[index] = T(v_reshape[i, j] - v_L[i, j]) # Constraint that the surface must be above the obstruction
+                index = index + 1
+            end 
+        end 
+        for j in 1:ny
+            c[index] = T(v_reshape[1, j]) # Constraint: when x=1 or x=nx, the surface is set to 0
+            index = index + 1
+            c[index] =  T(v_reshape[nx, j]) # Constraint: when x=1 or x=nx, the surface is set to 0
+            index = index + 1
+        end 
+        for i in 1:nx
+            c[index] = T(v_reshape[i, 1] - 1 + (2 * i -1)^2) # Constraint: when y=1 or y=ny, the surface follows the function " 1 + (2 * x -1)^2 "
+            index = index + 1
+            c[index] = T(v_reshape[i, ny] - 1 + (2 * i -1)^2) # Constraint: when y=1 or y=ny, the surface follows the function " 1 + (2 * x -1)^2 "
+            index = index + 1
+
+        end 
+        return c
+    end
+
+
+    lcon = zeros(T, nx * ny + 2 * nx + 2 * ny) # Lower bound all equal to 0
+    ucon = zeros(T, nx * ny + 2 * nx + 2 * ny) # Creation of the upper bound vector
+    ucon[1 : ny * nx] = Inf * ones(T, nx * ny) # first part equal to infinity
+    ucon[nx * ny + 1 : end] = zeros(T, 2 * nx + 2 * ny) # second part part equal to zero
+
+    v = vec(v_D) #convert to vector
+
+    nlp = ADNLPModel(Objective, v, constraints, lcon, ucon)
+    return nlp
+end 
+
+

src/Meta/minimalsurface.jl

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+minimalsurface_meta = Dict(
+    :nvar => 400,
+    :variable_nvar => false,
+    :ncon => 480,
+    :variable_ncon => false,
+    :minimize => true,
+    :name => "minimalsurface",
+    :has_equalities_only => false,
+    :has_inequalities_only => false,
+    :has_bounds => false,
+    :has_fixed_variables => false,
+    :objtype => :other,
+    :contype => :general,
+    :best_known_lower_bound => -Inf,
+    :best_known_upper_bound => Inf,
+    :is_feasible => missing,
+    :defined_everywhere => missing,
+    :origin => :unknown,
+
+)
+get_minimalsurface_nvar(; n::Integer = default_nvar, kwargs...) = 400
+get_minimalsurface_ncon(; n::Integer = default_nvar, kwargs...) = 480
+get_minimalsurface_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_minimalsurface_nnln(; n::Integer = default_nvar, kwargs...) = 480
+get_minimalsurface_nequ(; n::Integer = default_nvar, kwargs...) = 80
+get_minimalsurface_nineq(; n::Integer = default_nvar, kwargs...) = 400