Add the examples

Author: MohamedLaghdafHABIBOULLAH

.gitignore

@@ -0,0 +1 @@
+paper/examples/Manifest.toml

paper/examples/Project.toml

@@ -0,0 +1,18 @@
+[deps]
+ADNLPModels = "54578032-b7ea-4c30-94aa-7cbd1cce6c9a"
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
+MLDatasets = "eb30cadb-4394-5ae3-aed4-317e484a6458"
+NLPModels = "a4795742-8479-5a88-8948-cc11e1c8c1a6"
+NLPModelsModifiers = "e01155f1-5c6f-4375-a9d8-616dd036575f"
+ProximalOperators = "a725b495-10eb-56fe-b38b-717eba820537"
+RegularizedOptimization = "196f2941-2d58-45ba-9f13-43a2532b2fa8"
+RegularizedProblems = "ea076b23-609f-44d2-bb12-a4ae45328278"
+ShiftedProximalOperators = "d4fd37fa-580c-4e43-9b30-361c21aae263"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[compat]
+NLPModels = "0.19, 0.20, 0.21"
+NLPModelsModifiers = "0.7"
+ProximalOperators = "0.15"
+RegularizedProblems = "0.1"
+ShiftedProximalOperators = "0.2"

paper/examples/example1.jl

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+using LinearAlgebra, Random
+using ProximalOperators
+using NLPModels, NLPModelsModifiers, RegularizedProblems, RegularizedOptimization
+using MLDatasets
+
+random_seed = 1234
+Random.seed!(random_seed)
+
+# Load MNIST from MLDatasets
+imgs, labels = MLDatasets.MNIST.traindata()
+
+# Use RegularizedProblems' preprocessing
+A, b = RegularizedProblems.generate_data(imgs, labels, (1, 7), false)
+
+# Build the models
+model, _, _ = RegularizedProblems.svm_model(A, b)
+
+# Define the Hessian approximation
+f = LBFGSModel(model)
+
+# Define the nonsmooth regularizer (L0 norm)
+λ = 1.0e-1
+h = NormL0(λ)
+
+# Define the regularized NLP model
+reg_nlp = RegularizedNLPModel(f, h)
+
+# Choose a solver (R2DH) and execution statistics tracker
+solver_r2dh= R2DHSolver(reg_nlp)
+stats = RegularizedExecutionStats(reg_nlp)
+
+# Solve the problem 
+solve!(solver_r2dh, reg_nlp, stats, x = f.meta.x0, σk = 1e-6, atol = 2e-5, rtol = 2e-5, verbose = 1)
+
+@test stats.status == :first_order

paper/examples/example2.jl

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+## After merging the PRs on TR
+
+using LinearAlgebra
+using DifferentialEquations, ProximalOperators
+using ADNLPModels, NLPModels, NLPModelsModifiers, RegularizedOptimization, RegularizedProblems
+
+# Define the Fitzhugh-Nagumo problem
+model, _, _ = RegularizedProblems.fh_model()
+
+# Define the Hessian approximation
+f = LBFGSModel(fh_model)
+
+# Define the nonsmooth regularizer (L1 norm)
+λ = 0.1
+h = NormL1(λ)
+
+# Define the regularized NLP model
+reg_nlp = RegularizedNLPModel(f, h)
+
+# Choose a solver (TR) and execution statistics tracker
+solver_tr = TRSolver(reg_nlp)
+stats = RegularizedExecutionStats(reg_nlp)
+
+# Solve the problem
+solve!(solver_tr, reg_nlp, stats, x = f.meta.x0, atol = 1e-3, rtol = 1e-4, verbose = 10, ν = 1.0e+2)
+
+@test stats.status == :first_order

paper/paper.md

@@ -87,7 +87,7 @@ In contrast, many problems admit efficient implementations of Hessian–vector o
 
 ## In-place methods
 
-All solvers in **RegularizedOptimization.jl** are implemented in an in-place fashion, minimizing memory allocations and improving performance.
+All solvers in **RegularizedOptimization.jl** are implemented in an in-place fashion, minimizing memory allocations during the resolution process.
 
 # Examples
 
@@ -103,14 +103,20 @@ where $\lambda = 10^{-1}$ and $A \in \mathbb{R}^{m \times n}$, with $n = 784$ re
 ```julia
 using LinearAlgebra, Random
 using ProximalOperators
-using NLPModels, NLPModelsModifiers, RegularizedProblems, RegularizedOptimization, SolverCore
+using NLPModels, NLPModelsModifiers, RegularizedProblems, RegularizedOptimization
 using MLDatasets
 
 random_seed = 1234
 Random.seed!(random_seed)
 
-# Load the MNIST dataset
-model, _, _  = RegularizedProblems.svm_train_model()
+# Load MNIST from MLDatasets
+imgs, labels = MLDatasets.MNIST.traindata()
+
+# Use RegularizedProblems' preprocessing
+A, b = RegularizedProblems.generate_data(imgs, labels, (1, 7), false)
+
+# Build the models
+model, _, _ = RegularizedProblems.svm_model(A, b)
 
 # Define the Hessian approximation
 f = LBFGSModel(model)
@@ -135,12 +141,12 @@ Another example is the FitzHugh-Nagumo inverse problem with an $\ell_1$ penalty,
 
 ```julia
 using LinearAlgebra
-using DifferentialEquations, ProximalOperators
-using ADNLPModels, NLPModels, NLPModelsModifiers, RegularizedOptimization, RegularizedProblems
+using ProximalOperators
+using NLPModels, NLPModelsModifiers, RegularizedProblems, RegularizedOptimization
+using DifferentialEquations, ADNLPModels
 
-# Define the Fitzagerald Higgs problem
-data, _, _, _, _ = RegularizedProblems.FH_smooth_term()
-fh_model = ADNLPModel(misfit, ones(5))
+# Define the Fitzhugh-Nagumo problem
+model, _, _ = RegularizedProblems.fh_model()
 
 # Define the Hessian approximation
 f = LBFGSModel(fh_model)