For the fast approximate solution of Mixed-Integer Non-Linear Programs (MINLPs) arising in the context of Mixed-Integer Optimal Control Problems (MIOCPs) a decomposition algorithm exists that solves a sequence of three comparatively less hard subproblems to determine an approximate MINLP solution. In this work, we propose a problem formulation for the second algorithm stage that is a convex approximation of the original MINLP and relies on the Gauss-Newton approximation. We analyze the algorithm in terms of approximation properties and establish a first-order consistency result. Then, we investigate the proposed approach considering an illustrative numerical example of Mixed-Integer Optimal Control (MIOC) of a simple nonlinear and unstable system and considering a more complex application that is a numerical case study of MIOC of a renewable energy system. The investigation shows that the proposed formulation can yield an improved integer solution regarding the objective of the original MINLP compared with the Combinatorial Integral Approximation (CIA) algorithm.

## Citation

Preprint submitted to Automatica, 2022.