Features

The implementation has the following features:

• Choice of transcription method: global pseudospectral collocation (Legendre, Chebyshev, Radau or Gauss), local discretisation (trapezoidal or Hermite–Simpson), or integrated-residual transcription.

• Large-scale nonlinear programming using IPOPT, with an optional interface to SNOPT.

• Automatic first and second derivatives using the CppAD automatic differentiation library.

• Optional numerical differentiation using sparse finite differences, for both the Jacobian and the Hessian.

• Automatic identification of the sparsity of the derivative matrices.

• Estimation of the discretisation error.

• Automatic mesh refinement: Betts’ mesh refinement method for local discretisations, and hp-adaptive mesh refinement for pseudospectral discretisations (Radau, Gauss, Legendre and Chebyshev), which adjusts both the number of mesh intervals and the polynomial degree within each interval to meet a specified accuracy.

• Integrated-residual transcription, useful for problems with singular arcs or non-smooth solutions.

• Estimation of the costate (adjoint) variables, which allows solutions to be checked against the necessary conditions of optimality.

• Automatic scaling.

• DAE formulation, so that differential and algebraic constraints can be implemented in the same C++ function.

• A Python interface, enabling users to create and solve models without writing any C++, while benefiting from the speed of PSOPT’s C++ computational engine.

• Easy to use interface to GNUplot to produce graphical output, including 2D plots, 3D curves and surfaces, and polar plots.

• Automatic generation of LaTeX code to produce a table that summarises the mesh refinement process.

• Continuous integration testing on GitHub Actions: every change to the code triggers a full build and a test run of selected examples, with results compared against reference values.