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

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