OptimaSolver.jl

OptimaSolver is a Julia-native primal-dual interior-point solver for Gibbs-energy minimisation in equilibrium chemistry.

It solves problems of the form

\[\min_{n \in \mathbb{R}^{n_s}}\ f(n, p) \qquad \text{subject to} \qquad A n = b,\quad n \geq \varepsilon\]

where $f$ is the Gibbs free energy (e.g. $G(n) = \sum_i n_i(\mu_i^0/RT + \ln n_i)$ for an ideal/dilute solution), $A \in \mathbb{R}^{m \times n_s}$ is the mass-conservation (stoichiometric) matrix, $b \in \mathbb{R}^m$ is the element-abundance vector, and $\varepsilon$ is a small positivity floor.

Key features

• Schur-complement Newton step — reduces the $(n_s+m)$-dimensional KKT system to an $m \times m$ system by exploiting the diagonal Hessian structure. For chemistry problems $m$ is typically the number of elements ($m \leq 15$), so this is a dramatic reduction.
• Filter line search — Wächter & Biegler (2006) filter method with Armijo sufficient decrease on the barrier objective.
• Variable stability classification — near-bound (absent) species receive reduced step sizes to avoid numerical blow-up near the positivity boundary.
• Implicit-differentiation sensitivity — post-solve computation of $\partial n^*/\partial b$ and $\partial n^*/\partial(\mu^0/RT)$ using the same Schur-complement factorisation as the last Newton step.
• Warm-start — consecutive solves (e.g. temperature scans, titration curves) reuse the previous solution as the starting point, typically halving the iteration count or more.
• ForwardDiff / AD compatibility — no Float64 casts; the entire solver stack is written in generic Julia arithmetic so thermodynamic parameters can be differentiated through the solver.
• SciML drop-in — OptimaOptimizer implements SciMLBase.AbstractOptimizationAlgorithm and is a drop-in replacement for IpoptOptimizer in ChemistryLab.jl.

Lineage

OptimaSolver is a Julia port of the optima C++ library developed by Allan Leal (ETH Zürich):

https://github.com/reaktoro/optima

The algorithmic design — Schur-complement reduction, filter line search, variable stability classification, and implicit-differentiation sensitivity — originates from that library and from the following reference:

Leal, A.M.M., Blunt, M.J., LaForce, T.C. (2014). Efficient chemical equilibrium calculations for geochemical speciation and reactive transport modelling. Geochimica et Cosmochimica Acta, 131, 301–322. https://doi.org/10.1016/j.gca.2014.01.006

The Julia port was authored by Jean-François Barthélémy (CEREMA, France) with assistance from Claude Code (Anthropic).

Documentation structure

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