We consider models based on conservation laws. For the optimizationof such systems, a sensitivity analysis is essential to determinehow changes in the decision variables influence the objectivefunction. Here we study the sensitivity with respect to the initialdata of objective functions that depend upon the solution of Riemannproblems with piecewise linear flux functions. We presentrepresentations for the one–sided directional derivatives of theobjective functions. The results can be used in the numerical methodcalled Front-Tracking.
