Added online optimization tutorial+example, moved tutorials to an outer folder, updated project.toml to latest versions of the packages

Author: Shuvomoy

.gitignore

@@ -0,0 +1,5 @@
+*.minted
+*.gz
+*.aux
+*.listing
+*.log

Manifest.toml

@@ -1,6 +1,6 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.12.0"
+julia_version = "1.12.2"
 manifest_format = "2.0"
 project_hash = "1f0c6c59d478b4871cf7367edd9839c140f2da18"
 
@@ -36,9 +36,9 @@ version = "1.0.9+0"
 
 [[deps.COPT]]
 deps = ["LazyArtifacts", "Libdl", "LinearAlgebra", "MathOptInterface", "Pkg", "Random", "SparseArrays"]
-git-tree-sha1 = "9ebf6731777c6eb8e1beafc8d2803391cf77f619"
+git-tree-sha1 = "d155cf351bddde7f875f1f52688c159c4087d4a3"
 uuid = "227a2e2d-e949-4d8e-a1da-7384fe6f0b9f"
-version = "1.1.29"
+version = "1.1.30"
 
 [[deps.Clarabel]]
 deps = ["AMD", "DataStructures", "GenericLinearAlgebra", "JSON", "LinearAlgebra", "MathOptInterface", "Printf", "QDLDL", "SnoopPrecompile", "SparseArrays", "StaticArrays", "SuiteSparse", "TOML", "TimerOutputs"]
@@ -56,9 +56,9 @@ version = "0.11.0"
 
 [[deps.CodeTracking]]
 deps = ["InteractiveUtils", "UUIDs"]
-git-tree-sha1 = "9ce926a33a8608421a4d45c012884165b3fcd3ee"
+git-tree-sha1 = "b7231a755812695b8046e8471ddc34c8268cbad5"
 uuid = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2"
-version = "2.0.2"
+version = "3.0.0"
 
 [[deps.CodecBzip2]]
 deps = ["Bzip2_jll", "TranscodingStreams"]
@@ -129,7 +129,7 @@ version = "0.9.5"
 [[deps.Downloads]]
 deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
-version = "1.6.0"
+version = "1.7.0"
 
 [[deps.ExprTools]]
 git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
@@ -210,9 +210,9 @@ version = "1.29.3"
 
 [[deps.JuliaInterpreter]]
 deps = ["CodeTracking", "InteractiveUtils", "Random", "UUIDs"]
-git-tree-sha1 = "b6c76964c65ebf8309460fb8f0f437b4a59d809b"
+git-tree-sha1 = "80580012d4ed5a3e8b18c7cd86cebe4b816d17a6"
 uuid = "aa1ae85d-cabe-5617-a682-6adf51b2e16a"
-version = "0.10.7"
+version = "0.10.9"
 
 [[deps.JuliaSyntaxHighlighting]]
 deps = ["StyledStrings"]
@@ -232,7 +232,7 @@ version = "0.6.4"
 [[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
-version = "8.11.1+1"
+version = "8.15.0+0"
 
 [[deps.LibGit2]]
 deps = ["LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
@@ -286,9 +286,9 @@ version = "1.11.0"
 
 [[deps.LoweredCodeUtils]]
 deps = ["CodeTracking", "Compiler", "JuliaInterpreter"]
-git-tree-sha1 = "e24491cb83551e44a69b9106c50666dea9d953ab"
+git-tree-sha1 = "65ae3db6ab0e5b1b5f217043c558d9d1d33cc88d"
 uuid = "6f1432cf-f94c-5a45-995e-cdbf5db27b0b"
-version = "3.4.4"
+version = "3.5.0"
 
 [[deps.MacroTools]]
 git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522"
@@ -301,10 +301,10 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 version = "1.11.0"
 
 [[deps.MathOptInterface]]
-deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "DataStructures", "ForwardDiff", "JSON3", "LinearAlgebra", "MutableArithmetics", "NaNMath", "OrderedCollections", "PrecompileTools", "Printf", "SparseArrays", "SpecialFunctions", "Test"]
-git-tree-sha1 = "a2cbab4256690aee457d136752c404e001f27768"
+deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "ForwardDiff", "JSON3", "LinearAlgebra", "MutableArithmetics", "NaNMath", "OrderedCollections", "PrecompileTools", "Printf", "SparseArrays", "SpecialFunctions", "Test"]
+git-tree-sha1 = "181c2611c7aa6a362fdf937b1e2af55e6691181f"
 uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
-version = "1.46.0"
+version = "1.48.0"
 
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
@@ -366,7 +366,7 @@ version = "0.8.7+0"
 [[deps.OpenSSL_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "3.5.1+0"
+version = "3.5.4+0"
 
 [[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
@@ -380,7 +380,7 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.8.1"
 
 [[deps.PEPit]]
-deps = ["Clarabel", "JuMP", "LinearAlgebra", "Literate", "Mosek", "MosekTools", "OffsetArrays", "OrderedCollections", "Revise"]
+deps = ["COPT", "Clarabel", "JuMP", "LinearAlgebra", "Literate", "Mosek", "MosekTools", "OffsetArrays", "OrderedCollections", "Revise"]
 path = "."
 uuid = "362dabbc-d565-4ef8-96fa-aefabe1c072a"
 version = "1.0.0-DEV"
@@ -446,9 +446,9 @@ version = "1.3.1"
 
 [[deps.Revise]]
 deps = ["CodeTracking", "FileWatching", "JuliaInterpreter", "LibGit2", "LoweredCodeUtils", "OrderedCollections", "REPL", "Requires", "UUIDs", "Unicode"]
-git-tree-sha1 = "f0da88fc9f0825bba02a6edc28df68f22060c4c7"
+git-tree-sha1 = "ff0bd131abc4ebd9b66d2033144bed6d011d5074"
 uuid = "295af30f-e4ad-537b-8983-00126c2a3abe"
-version = "3.12.2"
+version = "3.12.3"
 
     [deps.Revise.extensions]
     DistributedExt = "Distributed"
@@ -588,14 +588,14 @@ version = "1.3.1+2"
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
-version = "5.13.1+1"
+version = "5.15.0+0"
 
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
 version = "1.64.0+1"
 
 [[deps.p7zip_jll]]
-deps = ["Artifacts", "Libdl"]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
-version = "17.5.0+2"
+version = "17.7.0+0"

examples/online_learning/online_gradient_descent.jl

@@ -0,0 +1,50 @@
+using PEPit, OrderedCollections
+
+function wc_online_gradient_descent(M::Real, D::Real, n::Int; verbose = true)
+
+    problem = PEP()
+
+    gamma = D / (M * sqrt(n))
+
+    fis = [declare_function!(problem, ConvexLipschitzFunction, OrderedDict("M" => M)) for _ in 1:n]
+
+    h = declare_function!(problem, ConvexIndicatorFunction, OrderedDict("D" => D))
+
+    F = sum(fis)
+
+    x_ref = set_initial_point!(problem)
+    x_ref, _, _ = proximal_step!(x_ref, h, 1)
+    _, F_ref = oracle!(F, x_ref)
+
+    x = set_initial_point!(problem)
+    x, _, _ = proximal_step!(x, h, 1)
+
+    f_saved = Vector{Expression}(undef, n)
+    for i in 1:n
+        g_i, f_i = oracle!(fis[i], x)
+        f_saved[i] = f_i
+        x, _, _ = proximal_step!(x - gamma * g_i, h, gamma)
+    end
+
+    set_performance_metric!(problem, sum(f_saved) - F_ref)
+
+    pepit_tau = solve!(problem; verbose=verbose)
+
+    theoretical_tau = M * D * sqrt(n)
+
+    if verbose != -1
+        println("*** Example file: worst-case regret of online gradient descent for fixed step-sizes ***")
+        println("\tPEPit guarantee:\t R_n <= $(round(pepit_tau, digits=6))")
+        println("\tTheoretical guarantee:\t R_n <= $(round(theoretical_tau, digits=6))")
+    end
+
+    return pepit_tau, theoretical_tau
+end
+
+
+
+M, D, n = 1.0, 0.5, 2
+
+pepit_tau, theoretical_tau = wc_online_gradient_descent(M, D, n; verbose=true)
+
+

src/PEPit.jl

@@ -39,6 +39,7 @@ include("core/psd_matrix.jl")
 include("core/function.jl")
 
 include("functions/convex_function.jl")
+include("functions/convex_lipschitz_function.jl")
 include("functions/smooth_function.jl")
 include("functions/smooth_convex_function.jl")
 include("functions/smooth_strongly_convex_function.jl")
@@ -62,11 +63,10 @@ include("primitive_steps/proximal_step.jl")
 include("primitive_steps/linear_optimization_step.jl")
 include("primitive_steps/shifted_optimization_step.jl")
 
-
 export
     PEP, Point, Expression, Constraint, PSDMatrix,
     AbstractFunction, PEPFunction,
-    ConvexFunction, SmoothFunction, SmoothConvexFunction, SmoothStronglyConvexFunction, StronglyConvexFunction, ConvexIndicatorFunction,
+    ConvexFunction, ConvexLipschitzFunction, SmoothFunction, SmoothConvexFunction, SmoothStronglyConvexFunction, StronglyConvexFunction, ConvexIndicatorFunction,
     LipschitzOperator, LinearOperator, NonexpansiveOperator, MonotoneOperator,
     solve!, declare_function!, set_initial_point!, set_initial_condition!,
     set_performance_metric!, add_constraint!, add_psd_matrix!,