GPOPS-II (pronounced "GPOPS 2") is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse nonlinear programming.

The acronym GPOPS stands for "General Purpose OPtimal Control Software", and the Roman numeral "II" refers to the fact that GPOPS-II is the second software of its type (that employs Gaussian quadrature integration).

GPOPS-II[3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where

It is noted that the approach to linking phases is based on well-known formulations in the literature.

in each phase is divided, and LGR collocation is performed in each interval.

Because the mesh can be adapted such that both the degree of the polynomial used to approximate the state

The code development name for the software was OptimalPrime, but was changed to GPOPS-II in late 2012 in order to keep with the lineage of the original version of GPOPS [12] which implemented global collocation using the Gauss pseudospectral method.

The development of GPOPS-II continues today, with improvements that include the open-source algorithmic differentiation package ADiGator [13] and continued development of

Published academic research where GPOPS-II has been used includes Refs.

[14][15][16] where the software has been used in applications such as performance optimization of Formula One race cars, Ref.

[17] where the software has been used for minimum-time optimization of low-thrust orbital transfers, Ref.