On Lagrange Multiplier Theorems for Non-smooth Optimization for a Large Class of Variational Models in Banach Spaces (Contemporary Mathematics, 2023)
This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality constraints and, in a second step, a more general model with equality and inequality constraints, always in a general Banach space context. We highlight some novelties are introduced related to the proof procedures developed in this text, which are in general softer than those concerning the present literature.
Keywords: non-smooth optimization; Lagrange multiplier theorems; equality and inequality constraints