The solver ecosystem in JSO is in constant development. We are looking into unifying the solver structure to make solvers, subsolvers, and tools plug-and-play.
Within JSO, our solver development has focused on three types of packages:
New methods, usually accompanied by research papers;
our implementation of (well- or no-so-well-)known methods;
wrappers around noteworthy solvers implemented in other languages.
Below is the list of solvers and the type of problems that they are designed to solve.
| Solver | Package | Description | Types of problem |
|---|
cannoles | CaNNOLeS.jl | Regularization method for nonlinear least squares | Equality-constrained NLS |
dci | DCISolver.jl | Trust-cylinder similar to two-step SQP | Equality-constrained NLP |
lbfgs | JSOSolvers.jl | Factorization-free linesearch limited-memory inverse BFGS | Unconstrained NLP |
percival | Percival.jl | Factorization-free augmented Lagrangian | Generally-constrained NLP |
ripqp | RipQP.jl | Regularized Interior-Point Quadratic Programming | Convex QP (incl. LP) |
tron | JSOSolvers.jl | Factorization-free trust-region second-order or quasi-Newton method | Bound-constrained NLP |
tronls | JSOSolvers.jl | Least-squares versions of tron | Unconstrained NLS |
trunk | JSOSolvers.jl | Factorization-free trust-region second-order or quasi-Newton method | Unconstrained NLP |
trunkls | JSOSolvers.jl | Least-squares version of trunk | Unconstrained NLS |
Our optimization problems can be defined as
\[\text{minimize} \quad f(x) \quad \text{subject to} \quad x \in \Omega.\]
Our constraint types and their meanings are:
Unconstrained: \(\Omega = \mathbb R^n\).
Bound constrained: \(\Omega = \{x \in \mathbb R^n |\ \ell \leq x \leq u\}\).
Equality constrained: \(\Omega = \{x \in \mathbb R^n |\ c(x) = 0\}\).
Generally constrained: \(\Omega = \{x \in \mathbb R^n |\ c_L \leq c(x) \leq c_U \}\), where \(c_{L_i} = c_{U_i}\) is a valid possibility, as are \(c_{L_i} = -\infty\) and \(c_{U_i} = \infty\), but not at the same time.
In addition to differences in the constraints, we also have different objective types:
NLP: General objective. The objective \(f(x)\) of these problems has no special structure to exploit. Access to its derivatives occurs through the default NLPModels.jl API.
NLS: Nonlinear Least-Squares problems. These problems are defined by \(f(x) = \tfrac{1}{2}\Vert F(x)\Vert^2\), with \(F\) and its derivatives available through the API for NLSModels, part of NLPModels.jl
QP: Quadratic Programming. These problems are defined by \(f(x) = \tfrac{1}{2}x^T Q x + g^T x + c\), with the API defined by QuadraticModels.jl.