  In this paper, we address the problem of local search for the falsification
of hybrid automata with affine dynamics. Namely, if we are given a sequence of
locations and a maximum simulation time, we return the trajectory that comes
the closest to the unsafe set. In order to solve this problem, we formulate it
as a differentiable optimization problem which we solve using Sequential
Quadratic Programming. The purpose of developing such a local search method is
to combine it with high level stochastic optimization algorithms in order to
falsify hybrid systems with complex discrete dynamics and high dimensional
continuous spaces. Experimental results indicate that indeed the local search
procedure improves upon the results of pure stochastic optimization algorithms.
