A regularization method for constrained nonlinear least squares

A Julia Implementation of Algorithm NCL for Constrained Optimization

“…The main advantage of a Julia implementation over our original AMPL implementation is that we may take full advantage of our Julia software suite for optimization, hosted under the JuliaSmoothOptimizers (JSO) organization [22]. Our suite provides a general consistent API for solvers to interact with models by providing flexible data types to represent the objective and constraint functions, to evaluate their derivatives, to examine bounds on the variables, to add slack variables transparently, and to provide essentially any information that a solver might request from a model.…”

“…• NLPModels [24] is the main modeling package that defines the API on which solvers can rely to interact with models. Models are represented as instances of a data type deriving from the base type AbstractNLPModel, and solvers can evaluate the objective value by calling the obj() method, the gradient vector by calling the grad() method, and so forth.…”

“…• NLPModelsIpopt [23] is a thin translation layer between the low-level Julia interface to IPOPT provided by the IPOPT.jl package 4 and NLPModels, and lets users solve any problem conforming to the NLPModels API with IPOPT.…”

“…• NLPModelsKnitro [25] is similar to NLPModelsIpopt, but lets users solve problems with KNITRO via the low-level interface provided by KNITRO.jl. 5 Julia is a convenient language built on top of state-of-the-art infrastructure underlying modern compilers such as Clang.…”

A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems

“…In particular, the work of Izmailov et al [15] is concerned with local convergence properties of Tikhonov-type regularization algorithms, which requires the use of second derivatives. Meanwhile, other regularization techniques for constrained least squares that do not directly belong to the Levenberg-Marquardt class of methods have recently been proposed, that are also based on the SQP methodology (see [17,22] and references therein). However, to the best of our knowledge, these approaches are not based on nonmonotone rules, and generally require second-order derivatives.…”