# A Sequential Convex Programming Approach to Solving Quadratic Programs and Optimal Control Problems with Linear Complementarity Constraints

arXiv: https://arxiv.org/abs/2103.05965 · HTML: https://mlsanity.com/paper/2103.05965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [A neural network-based approach to hybrid systems identification for control](https://mlsanity.com/paper/2404.01814/) (2024)

## Abstract (arXiv)

Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with linear complementarity constraints. A novel approach to solving a penalty reformulation using sequential convex programming and a homotopy on the penalty parameter is introduced. Linearizing the necessarily nonconvex penalty function yields convex quadratic subproblems, which have a constant Hessian matrix throughout all iterates. This allows solution computation with a single KKT matrix factorization. Furthermore, a globalization scheme is introduced in which the underlying merit function is minimized analytically, and guarantee of descent is provided at each iterate. The algorithmic features and possible computational speedups are illustrated in a numerical experiment.