The method of Lagrange multipliers for the class of subsmooth mappings (Q1646380)

The author extends the classical Lagrange method to the wide class of so-called subsmooth mappings in Banach spaces; these mappings are related to the notion of strong compact subdifferential introduced recently in his paper. He also relies on his paper [ibid. 99, No. 4, 619--622 (2016; Zbl 1362.47052); translation from Mat. Zametki 99, No. 4, 631--634 (2016)] dealing with the generalization to this class of inverse and implicit mapping theorems. As an application, he shows the transversality conditions for the variational functional with moving boundary with subsmooth Lagrangian and a constraint of similar type.