The first Weierstrass-Erdmann condition in variational problems involving differential inclusions

Abstract

Abstract. In this paper, the authors continue a previous study about the broken extremals in variational problems with differential inclusions. In said paper, we presented a necessary condition for extremals with corner points that is valid for shapeable sets. This condition has been obtained by adapting a novel proof of the first Weiertrass-Erdmann condition.In the present paper we extend the class of shapeable sets and demonstrate that the setwith G 1 , G 2 ∈ C 1 , is shapeable for every t .Finally, we present two examples, the second being a classic engineering problem: the optimization of hydrothermal systems.Mathematics subject classification (2000): 49K24, 49K30.

Cyclic coordinate descent in hydrothermal nonsmooth problems

“…Proof Considering that q * i minimizes the functional J i q , and the results obtained in [14] for those points where L i q ż i is continuous and in [8] for those points of discontinuity of L i q ż i (existence of plants with pumping capacity), we may guarantee that the minimum of the proposed problem belongs to C 1 . Therefore, i (q) is of class C 1 .…”