# Convex Optimization of Launch Vehicle Ascent Trajectory with Heat-Flux and Splash-Down Constraints

arXiv: https://arxiv.org/abs/2008.13239 · HTML: https://mlsanity.com/paper/2008.13239/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [A Machine Learning Surrogate Modeling Benchmark for Temperature Field Reconstruction of Heat-Source Systems](https://mlsanity.com/paper/2108.08298/) (2021)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Joint Deep Reversible Regression Model and Physics-Informed Unsupervised Learning for Temperature Field Reconstruction](https://mlsanity.com/paper/2106.11929/) (2021)
- [Learning to Reconstruct Temperature Field from Sparse Observations with Implicit Physics Priors](https://mlsanity.com/paper/2512.01196/) (2025)

## Abstract (arXiv)

This paper presents a convex programming approach to the optimization of a multistage launch vehicle ascent trajectory, from the liftoff to the payload injection into the target orbit, taking into account multiple nonconvex constraints, such as the maximum heat flux after fairing jettisoning and the splash-down of the burned-out stages. Lossless and successive convexification are employed to convert the problem into a sequence of convex subproblems. Virtual controls and buffer zones are included to ensure the recursive feasibility of the process and a state-of-the-art method for updating the reference solution is implemented to filter out undesired phenomena that may hinder convergence. A hp pseudospectral discretization scheme is used to accurately capture the complex ascent and return dynamics with a limited computational effort. The convergence properties, computational efficiency, and robustness of the algorithm are discussed on the basis of numerical results. The ascent of the VEGA launch vehicle toward a polar orbit is used as case study to discuss the interaction between the heat flux and splash-down constraints. Finally, a sensitivity analysis of the launch vehicle carrying capacity to different splash-down locations is presented.