>Those comments explain how to reformulate the Pontryagin Maximum Principle for abnormal problems. Please tell? I have yet to see anyone give a satisfactory ap

>Those comments explain how to reformulate the Pontryagin Maximum Principle for abnormal problems. Please tell? I have yet to see anyone give a satisfactory approach on how to deal with the abnormal case. For context there are sometimes optimal solutions which are not given by Pontryagin's Maximum Principle (PMP). An analogous situation can occur with Lagrange multipliers. The necessary conditions given by the Lagrange multipliers are not related to the maximization of the object functional. I surely think the situation is worse with the PMP because you are now in a continuous setting. I think [0] offers some good discussion for the abnormal case in Lagrange multipliers. I would be interested if anyone has made any recent progress in dealing with the abnormal case for the PMP. [0] Optimality Conditions: Abnormal and Degenerate Problems By A.V. Arutyunov