R2NLS solver for unconstrained nonlinear least-squares (NLS) problems

Project.toml

@@ -3,25 +3,37 @@ uuid = "10dff2fc-5484-5881-a0e0-c90441020f8a"
 version = "0.14.1"
 
 [deps]
+Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
+GenericLinearAlgebra = "14197337-ba66-59df-a3e3-ca00e7dcff7a"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearOperators = "5c8ed15e-5a4c-59e4-a42b-c7e8811fb125"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 NLPModels = "a4795742-8479-5a88-8948-cc11e1c8c1a6"
 NLPModelsModifiers = "e01155f1-5c6f-4375-a9d8-616dd036575f"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+QRMumps = "422b30a1-cc69-4d85-abe7-cc07b540c444"
 SolverCore = "ff4d7338-4cf1-434d-91df-b86cb86fb843"
 SolverParameters = "d076d87d-d1f9-4ea3-a44b-64b4cdd1e470"
 SolverTools = "b5612192-2639-5dc1-abfe-fbedd65fab29"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SparseMatricesCOO = "fa32481b-f100-4b48-8dc8-c62f61b13870"
+TSVD = "9449cd9e-2762-5aa3-a617-5413e99d722e"
 
 [compat]
-Krylov = "0.10.0"
+Arpack = "0.5.4"
+GenericLinearAlgebra = "0.3.18"
+Krylov = "0.10.1"
 LinearOperators = "2.0"
 NLPModels = "0.21"
 NLPModelsModifiers = "0.7"
+QRMumps = "0.3.1"
 SolverCore = "0.3"
 SolverParameters = "0.1"
 SolverTools = "0.9"
+SparseArrays = "1.11.0"
+SparseMatricesCOO = "0.2.5"
+TSVD = "0.4.4"
 julia = "1.10"
 
 [extras]

README.md

@@ -34,6 +34,8 @@ This package provides an implementation of four classic algorithms for unconstra
     > high-order regularized models. *Mathematical Programming*, 163(1), 359-368.
     > DOI: [10.1007/s10107-016-1065-8](https://doi.org/10.1007/s10107-016-1065-8)
 
+- `R2NLS`: an inexact second-order quadratic regularization method for nonlinear least-squares problems;
+
 - `fomo`: a first-order method with momentum for unconstrained optimization;
 
 - `tron`: a pure Julia implementation of TRON, a trust-region solver for bound-constrained optimization described in

docs/src/solvers.md

@@ -11,7 +11,7 @@
 | Problem type          | Solvers  |
 | --------------------- | -------- |
 | Unconstrained NLP     | [`lbfgs`](@ref), [`tron`](@ref), [`trunk`](@ref), [`R2`](@ref), [`fomo`](@ref)|
-| Unconstrained NLS     | [`trunk`](@ref), [`tron`](@ref) |
+| Unconstrained NLS     | [`trunk`](@ref), [`tron`](@ref), [`R2NLS`](@ref)|
 | Bound-constrained NLP | [`tron`](@ref) |
 | Bound-constrained NLS | [`tron`](@ref) |
 
@@ -22,5 +22,6 @@ lbfgs
 tron
 trunk
 R2
+R2NLS
 fomo
 ```

src/JSOSolvers.jl

@@ -1,7 +1,7 @@
 module JSOSolvers
 
 # stdlib
-using LinearAlgebra, Logging, Printf
+using LinearAlgebra, Logging, Printf, Arpack, SparseArrays
 
 # JSO packages
 using Krylov,
@@ -10,6 +10,8 @@ using Krylov,
 import SolverCore.solve!
 export solve!
 
+include("utilities.jl")
+
 const Callback_docstring = "
 The callback is called at each iteration.
 The expected signature of the callback is `callback(nlp, solver, stats)`, and its output is ignored.
@@ -48,6 +50,8 @@ include("fomo.jl")
 
 # Unconstrained solvers for NLS
 include("trunkls.jl")
+include("R2NLS.jl")
+
 
 # List of keywords accepted by TRONTrustRegion
 const tron_keys = (